Same boat here.
Other than opening theory...

It depends on your current level of understanding, but if you are beginner to intermediate level, then chess opening principles might just be the huge opening knowledge you need (and is simple to implement without memorizing lines!)
https://www.chess.com/blog/KeSetoKaiba/opening-principles-again
If you are a bit more advanced than the fundamentals of chess opening principles, then the advanced player wanting to avoid so much opening theory memorization should choose an opening which is more reliant on common themes and patterns than specific move orders and sharp play.
Good openings to choose with more plans than theory would be openings like the King's Indian Defense (black), Dutch Defense (black), Queen's Gambit (white), Trompowsky (white), English Opening (white), London System (white), Hedgehog pawn formations (white or black, but I prefer it for black personally) and so on, but some of these openings are much more advanced in level of understanding, so it depends what your general chess knowledge and ability is.
Study classic games.
E.g. Nunn's "Understanding Chess Move by move" would be a start. "Fisher's 60 memorable games", etc.
Start playing real chess. You can probably get by with 30/0 games at first, but soon make a move to at least 60/0.
Work on solving tactics problems. Mates in 1-2-3 for starters.
Also, when playing games, for every move you're about to make, write down at least 2 more candidate moves (i.e. other good moves that you can find in this position).
Opening wise, the fundamentals should take you to 1600-ish, or so I'm told.
Good luck.

For this purpose, I've written this guide on how to improve from a beginner level:
https://www.chess.com/blog/nklristic/the-beginners-tale-first-steps-to-chess-improvement
I did it from my own experience, hopefully it will be useful to you. Good luck on your chess improvement.

Memorizing opening lines is absolutely not needed. "I try and play toward the middle and develop pieces" is good.
I have checked a lost game of yours, and it is clear that you just make a ton of 1-move blunders. These are obvious blunders even for a beginner.
https://www.chess.com/analysis/game/live/37312290521?tab=analysis
Move 3: white does not defend the e4 pawn, and you don't take it for whatever reason. The pawn is still hanging there for 4 more moves, and you never take it.
15. Nf6+ just loses the knight for no reason, but you don't take it.
Move 18: Your opponent's bishop is hanging on e6, but you don't take it, instead you make a random legal move. Now you are losing instead of winning.
23. - Kxf8 loses the queen for no reason. After 24. Rxf7 you could at least win a rook + bishop for the queen, but instead you let him take the queen for free.
Any one of those 1-move blunders is enough to completely ruin and lose a game, and you made a dozen of those. It seems to me that you are making random legal moves after "thinking" for 3-4-5 seconds, in a rapid game where you have a lot of time. You have to slow down, and think of your moves. Calculating 1 move ahead is not hard. You have to stop these blunders, nothing else matters at all.
I also recommend doing puzzles, that is the best and most fun way to improve your calculation skills.

Improving Your Chess - Resources for Beginners and Beyond...
https://www.chess.com/blog/RussBell/improving-your-chess-resources-for-beginners-and-beyond
https://www.chess.com/blog/RussBell
#1
"I don't have the mental acumen to memorize/understand openings or opening theory."
++ There is no need for opening theory. It even hinders improvement.
"how to improve?"
++ Train tactics. Analyse lost games. Study annotated grandmaster games. Study endgames.
"I try and play toward the middle and develop pieces" ++ That is good.
"but after the first 3-4 moves it seems like no man's land on how to proceed from there. "
++ You must think about the position. What are desirable positions for your pieces? What are desirable positions for his pieces? What trades would be good for you? What trades do you have to avoid? What pawns to move or not to move?
It’s because all of that is way down the road, and going over that stuff now is like studying calculus and differential equations before you even know order of operations. It’s a waste of time and is probably going to do more harm than good.
The number 1 thing to focus on as a true beginner (after the rules and how the pieces move) is board vision. You can study all that other stuff but if you’re skill at seeing the board is let’s say a 600 you’ll struggle to improve past that. It’s the lowest common denominator.
Note: I made this as a response to basically the same topic in a different thread but felt like it might be good advice in this one as well. Best of luck in your chess journey.
Old guy here. I don't have the mental acumen to memorize/understand openings or opening theory. That said, does anybody have any instruction on how to improve? I try and play toward the middle and develop pieces, but after the first 3-4 moves it seems like no man's land on how to proceed from there.