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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.