Usually, I just revert back to an old position, which can be somewhat jarring when the character is in free-fall and is moving in large enough steps that it ends up floating. Overall, the video with the adjustment that I stated works well for me (: I often just ignore the slight "floating", where the character dellerates, just before hitting a surface. I don't know if it would be possible to adapt the video's system in order to feature quarter steps, like is used in mario 64. That could prevent the jarring. I'm sorry that I'm not more knowledgable on other systems, but the one in the video, maybe with a few adaptations seemed to work well for me. I actually used it in a previous game jam game (admittedly which is not as good as yours), but if you want to try it, you can play it here: https://ossoace.itch.io/find-fakes or here: https://www.zel.us/games/fake_find/. Hopefully it helps! And, I'll have a look into your system. It sounds interesting!
Well, my code is probably hard to read, and just reverts the x-axis to it's old position.
If you want to find a better system, I think this game of mine: https://void-gamesplay.itch.io/the-return-of-timmy-the-grappling-hook has a pretty solid collision system.
Anyway, thanks for the help! Its made me think a bit about collisions without barging head first into the code.