After implementing a "slipping" feature that let moving objects slip through certain gaps if they were almost through, I rolled it back because it ended up being awkward. Instead, I took a look at Zelda and found out it was doing this
amazingly elegant thing and implemented that.
It needs tuning, as it moves the player back on grid a little too aggressively, but it's really nice that you can bump into a wall right next to a gap you wanted to go through and if you keep pressing left, it'll inch you through.