Hi!
Simply press space repeatedly (without holding any arrow keys) since the wall jump turn you around automatically it should work without any problems and be fairly consistent!
Please note that this game was made during a game jam on an engine not made AT ALL for platformers so things can be a little rough.
All the wall-jumps needed to complete the game are 2 tiles large which is enough to not have to move by yourself. If you're facing a 3 tiles large gap, you're not supposed to be going there (however you can, as you said, technically do the jump. Initially I wanted to hide stuff where the 3 tiles jumps are but ran out of time)
Here's a video showing a few wall-jumps : https://gfycat.com/UnsungNippyEskimodog, hope it helps you! Sorry you're having a bad experience, like I said in my previous message, things were pretty rough due to the engine used and time constraint.
