Some ROM hacks shift content of the save slightly, and that results in the save not being able to be used by sav hacking program. Most, if not all, save hacking programs only support official saves.
Here's an example of using your unedited save with PKHeX
This does not look normal.
(edit: I hope you didn't upload the wrong save under the wrong title. Besides the invalid box data, PKHeX is showing this unedited save to have invalid checksums over various blocks too)
As such, I would advise you to not use any save editing programs and expect it to work.
You could either:
1) Manually calculate the checksum of the parts, or
2) Use a cheat code to wipe your TM bag, or
3) Restart your game, and not activate too many cheats at one go in your new playthrough, or
4) Learn to live with it. Trade your mons to another save, where you can use TMs on it, then trade it back.
(I'm under the impression you activated too many cheats at one time. I once did that and have Balls in my Key Items, so I would know.)