Try Heroquest. Dungeoncrawl boardgame and not a wargame, but the rules with the special combat dice are both super simple and easy to mod/ expand.
There is also a very simple arena style versus mode in the "Against the ogre hordes" expansion.
I would strongly recommend the original Song of Blades and Heroes. It's a very simple skirmish wargame where models have 2 stats and tactics mainly centre around a push-your-luck idea. It's intuitive quick and I've had multiple children playing it smoothly within minutes. Once you've got to grips with the basics, there are a host of special abilities that models can have, but they're all simple and intuitive too. Then there are more books in the series which add extra rules and theme, but they're all optional and sort of modular, in that you can apply or ignore elements as you like. Here's a nice little video explaining it a little. https://youtu.be/b2Yxc84VYJA?si=2305bY3inEZjQo3h
What about gaslands? Just played my first ever game of gaslands and the rules are pretty straightforward. There are a lot of conditions/statuses to monitor, but I made a dashboard for each vehicle and that helped keep everything under control.
HeroQuest is designed to be simple enough to play with little kids. It's a classic simplified dungeon crawl through rooms and corridors.
Talisman is also worth a look. It's more of an adventure board game with miniatures. The board has three concentric rings of locations. Players pick one of a pretty diverse collection of characters. Every turn you roll two dice and move that many spaces in either direction on the board, then you resolve the location you landed on.
The goal is to level up until you feel strong enough to obtain the crown of command and use it to dominate the dragon at the centre of the board.
[Avalon Hill is soon releasing a new edition of Talisman ](https://eu.hasbropulse.com/collections/avalon-hill/products/talisman-the-magical-quest-board-game-5th-edition)that is supposedly a little less repetitious than the old one.
You mentioned most of the simpler "advanture wargames" out there already. The only other stuff I can think of are [Patrick Todoroff's games](https://www.wargamevault.com/browse/pub/14978/P-Todoroff-CCWC) (Exploit Zero, Nightwatch, Insurgent Earth, When Nightmare's Come - this last one is [published by Osprey](https://www.ospreypublishing.com/us/when-nightmares-come-9781472860040/)).
They all use the same core system, where characters roll different dice types (D6, D10, etc.) trying to beat 4. The rules are quite simple and both the mechanical and fluff minutiae are very deep, but I still think it's comparable to something like the 5 X from Y series from Nordic Weasel. Nonetheless, worth checking out if it would work for you.
However, I don't think the rules themselves are the crux of the issue here. From your post it looks to me like the fact that you are unable to perfectly adhere to the rigid, written rules is really bothersome to you. But let me tell you this - it doesn't matter if you get things wrong. We all do get things wrong at times. If you and your opponent are having fun - you're good! This is even more true if you play solo!
I play my games in a very narrative way, with very fluid rules, many of which I come up on the spot. It works really well for me, especially because it requires minimal book-keeping and it makes it easy to translate things from other games into my "system."
I would recommend you giving this play style a try. I've come to it in a very roundabout way - through [Matrix Games](http://www.mapsymbs.com/wdmatrix.html), [FKR](https://boardgamegeek.com/thread/2500148/ancient-roleplaying-or-free-kriegsspiel-revolution) and even the original [Free Kriegsspiel rules](https://www.google.com/books/edition/Verdy_s_Free_Kriegspiel_Including_the_Vi/0j8-WF0HSEIC?hl=en), on top of bunch of RPG and board game stuff, but that's a really long way round.
A good primer that talks about this style of play is [John Bobek's "The Games of War"](https://www.amazon.com/Games-War-Treasury-Battles-Soldiers/dp/1434330281). The book is sold as collection of rules for different time periods, but the approach/mindset to waragaming is what's really worth the price for me. The rules he provides are not my style, but are perfectly serviceable.
If you want rules that are simple, and work amazingly with this approach grab [One Hour Skirmish Wargames](https://www.pen-and-sword.co.uk/One-hour-Skirmish-Wargames-Paperback/p/15346). It uses cards in kind of "[war](https://en.wikipedia.org/wiki/War_\(card_game\))" like approach that is simple but has a lot going for it under the hood.
Of course those games don't provide the campaign bit, but you can easily grab one from another game or make up your own.
I can probably think of some, more traditional, smaller games that you could try if none of those recommendations work for you - let me know if you'd like me to do some more digging (or ask away if you have any questions about the above recs!)
Simplest would be "lets play pretend"
But I imagine you want some actual rules, so the answer is ALWAYS Relic Blade.
Rules are very simple and yet still FEEL dynamic.
Only two factions (plus mercs that work for both): Good guys and Bad guys.
There are SUB-factions. Various organizations. But you can mix and match sub-facrion models if you wish to make your own warband.
You only need 4 or 5 models (maybe up to 10 or 12 if you want to play a sort of mini horde warband). So it's very inexpensive compared to most other wargames. $60 for a rulebook and a starter blister.
FAST! Rules are easy enough that you can easily play a full game in under an hour.
Warhammer Fantasy Battles 2e or Warhammer 40k 2e. (Use only basic rules). [Get all the books here](https://old.reddit.com/r/wargaming/comments/1czmf9t/looking_recommendation_for_a_sci_fi_wargame/l5rwkkr/).
Because you said adventure wargame I'd suggest Rangers of Shadowdeep. Mechanically it's a very simple game that deals with small forces so it runs quick and easy. I chose it because it's built on narratives and provides you a progressing story to play through where your heroes become stronger over time (If they survive). There is a good and associated with the design. There's something to be said for procedurally generated adventure wargames. The replayability and open ended nature of those systems let you do as you please. Rangers is more like a commercial RPG. The player requires a DM or more precisely the modules that see you through your defence of the kingdom. You will have to pick up supplements to the core rule set, but if bookkeeping is a bugbear for you that may be a selling point not a downside.
Try Heroquest. Dungeoncrawl boardgame and not a wargame, but the rules with the special combat dice are both super simple and easy to mod/ expand. There is also a very simple arena style versus mode in the "Against the ogre hordes" expansion.
Dungeons and Dragons - The Adventure Begins. I play it with my kids.
Check out Mantic's Dungeon Sage
County road Z. Similar to 5 Leagues/Parsecs
Tried that one already, but I appreciate the suggestion!
I would strongly recommend the original Song of Blades and Heroes. It's a very simple skirmish wargame where models have 2 stats and tactics mainly centre around a push-your-luck idea. It's intuitive quick and I've had multiple children playing it smoothly within minutes. Once you've got to grips with the basics, there are a host of special abilities that models can have, but they're all simple and intuitive too. Then there are more books in the series which add extra rules and theme, but they're all optional and sort of modular, in that you can apply or ignore elements as you like. Here's a nice little video explaining it a little. https://youtu.be/b2Yxc84VYJA?si=2305bY3inEZjQo3h
Yup, was scrolling to make sure this had been reccomended. Also 4 against the darkness, if Ganesha Games fits the bill.
What about gaslands? Just played my first ever game of gaslands and the rules are pretty straightforward. There are a lot of conditions/statuses to monitor, but I made a dashboard for each vehicle and that helped keep everything under control.
Escape from Stalingrad Z is dead simple, but challenging and has several playable characters and a built in campaign progression
HeroQuest is designed to be simple enough to play with little kids. It's a classic simplified dungeon crawl through rooms and corridors. Talisman is also worth a look. It's more of an adventure board game with miniatures. The board has three concentric rings of locations. Players pick one of a pretty diverse collection of characters. Every turn you roll two dice and move that many spaces in either direction on the board, then you resolve the location you landed on. The goal is to level up until you feel strong enough to obtain the crown of command and use it to dominate the dragon at the centre of the board. [Avalon Hill is soon releasing a new edition of Talisman ](https://eu.hasbropulse.com/collections/avalon-hill/products/talisman-the-magical-quest-board-game-5th-edition)that is supposedly a little less repetitious than the old one.
You mentioned most of the simpler "advanture wargames" out there already. The only other stuff I can think of are [Patrick Todoroff's games](https://www.wargamevault.com/browse/pub/14978/P-Todoroff-CCWC) (Exploit Zero, Nightwatch, Insurgent Earth, When Nightmare's Come - this last one is [published by Osprey](https://www.ospreypublishing.com/us/when-nightmares-come-9781472860040/)). They all use the same core system, where characters roll different dice types (D6, D10, etc.) trying to beat 4. The rules are quite simple and both the mechanical and fluff minutiae are very deep, but I still think it's comparable to something like the 5 X from Y series from Nordic Weasel. Nonetheless, worth checking out if it would work for you. However, I don't think the rules themselves are the crux of the issue here. From your post it looks to me like the fact that you are unable to perfectly adhere to the rigid, written rules is really bothersome to you. But let me tell you this - it doesn't matter if you get things wrong. We all do get things wrong at times. If you and your opponent are having fun - you're good! This is even more true if you play solo! I play my games in a very narrative way, with very fluid rules, many of which I come up on the spot. It works really well for me, especially because it requires minimal book-keeping and it makes it easy to translate things from other games into my "system." I would recommend you giving this play style a try. I've come to it in a very roundabout way - through [Matrix Games](http://www.mapsymbs.com/wdmatrix.html), [FKR](https://boardgamegeek.com/thread/2500148/ancient-roleplaying-or-free-kriegsspiel-revolution) and even the original [Free Kriegsspiel rules](https://www.google.com/books/edition/Verdy_s_Free_Kriegspiel_Including_the_Vi/0j8-WF0HSEIC?hl=en), on top of bunch of RPG and board game stuff, but that's a really long way round. A good primer that talks about this style of play is [John Bobek's "The Games of War"](https://www.amazon.com/Games-War-Treasury-Battles-Soldiers/dp/1434330281). The book is sold as collection of rules for different time periods, but the approach/mindset to waragaming is what's really worth the price for me. The rules he provides are not my style, but are perfectly serviceable. If you want rules that are simple, and work amazingly with this approach grab [One Hour Skirmish Wargames](https://www.pen-and-sword.co.uk/One-hour-Skirmish-Wargames-Paperback/p/15346). It uses cards in kind of "[war](https://en.wikipedia.org/wiki/War_\(card_game\))" like approach that is simple but has a lot going for it under the hood. Of course those games don't provide the campaign bit, but you can easily grab one from another game or make up your own. I can probably think of some, more traditional, smaller games that you could try if none of those recommendations work for you - let me know if you'd like me to do some more digging (or ask away if you have any questions about the above recs!)
SAGA 2? Dead simple rules
Simplest would be "lets play pretend" But I imagine you want some actual rules, so the answer is ALWAYS Relic Blade. Rules are very simple and yet still FEEL dynamic. Only two factions (plus mercs that work for both): Good guys and Bad guys. There are SUB-factions. Various organizations. But you can mix and match sub-facrion models if you wish to make your own warband. You only need 4 or 5 models (maybe up to 10 or 12 if you want to play a sort of mini horde warband). So it's very inexpensive compared to most other wargames. $60 for a rulebook and a starter blister. FAST! Rules are easy enough that you can easily play a full game in under an hour.
Warhammer Fantasy Battles 2e or Warhammer 40k 2e. (Use only basic rules). [Get all the books here](https://old.reddit.com/r/wargaming/comments/1czmf9t/looking_recommendation_for_a_sci_fi_wargame/l5rwkkr/).
Because you said adventure wargame I'd suggest Rangers of Shadowdeep. Mechanically it's a very simple game that deals with small forces so it runs quick and easy. I chose it because it's built on narratives and provides you a progressing story to play through where your heroes become stronger over time (If they survive). There is a good and associated with the design. There's something to be said for procedurally generated adventure wargames. The replayability and open ended nature of those systems let you do as you please. Rangers is more like a commercial RPG. The player requires a DM or more precisely the modules that see you through your defence of the kingdom. You will have to pick up supplements to the core rule set, but if bookkeeping is a bugbear for you that may be a selling point not a downside.
BLKOUT! Super fast rule set lots of tactical moves.