So it doesn't seem to be related to the texture page size; changing the size shuffles the sprites a little, but the issue is obviously still there. What surprises me is that a couple sprites are correctly displayed... Maybe one of the texture groups is a bit too crowded.
I tried to make a couple more changes, and somehow managed to break the entire project... Is there a way to contact you on the weight gaming forums or reddit once I have figured out this mess? I don't use many social medias, so these are pretty much the only two options I have. It might take me a bit of time, but I want to try a few more things before giving up.