So, did some basic testing in the first area to refresh myself and make sure the basics were working right:
No defeats:
-Can unequip clips
-Can't unequip jacket
1 and 2 defeats: same
3 defeats:
-Can unequip jacket
-Can unequip clips, but it doesn't matter, they show up anyway when a fight starts. Canonically this is because Mezz is putting them on again without realizing it. Mezz is also much more vulnerable to hypno attacks at this point, and his own attacks are weaker.
So of all the stuff you described in your initial post, the only thing that isn't as it should be is the jacket: after 3 defeats, you should always be able to toggle that. What happens when you try to remove the jacket? Does he give the normal quip about not being that confident, or do you just get nothing after you drop out of the menu? I've tried a few different combos in terms of equip/unequip order without any luck, let me know if there's a particular one you're doing that's causing the jacket issue reliably.
Also, doesn't really matter for the bug, but since you were curious: I'm not swapping out characters, just modding stats via states. Things are a lot easier to keep track of that way. All the changed graphics are state-dependent.