Thank you for the quick and comprehensive reply! Unfortunately, I am still having the padding show up for some reason.
I did study that post, and the user-guide section for Texture Exporting, and it all seemed to make sense, but I guess it may have gone over my head.
I had tried many settings, but I think this experience will teach me to make better decisions about messing with settings; i.e. I'm going to make a spreadsheet to track and document any changes based on single settings changed, rather than try it, fail, change another setting, try, and fail again.
Even with 0 Padding, unchecking Edge padding, unchecking remove whitespace, switching to Grid, and unchecking Pre. Alpha(Thank you for explaining that, btw; it was kind of confusing in the guide), I still have this odd space between images.
At one point I thought it could have even been something to do with the version I was using, since I was sure I managed to get this working a few months ago; but changing the version didn't help, either. (Not that it should have worked, in the first place)
Attached Below are the settings I used this time, as per your instruction, and the results. This is quite puzzling.