Edit: Just tested:
-After 3 defeats through the new job, Mezz does correctly remove his clothes with the appropriate comments, and he does unequip them properly, not just change his sprite.
-Getting captured in the stealth version of ent. dist. 1 3 times does correctly strip Mezz, both visually and removing the jacket item, and recovery works correctly.
Can you confirm that you are sure you're on 1.0.2? Was playthrough done on an earlier version? There were duplication issues with the jacket previously which caused a variety of issues, but those have been fixed as of .2. If you can confirm this was all played through on .2, can you upload a save demonstrating it to catbox.moe or a similar site and link it here?
Also, in general try to report bugs on Substar, comments or dms there if the pack hasn't been released yet. Doesn't matter in this case, since there isn't really much of a spoiler concern, but just keep it in mind for the future.