Man, I have terrible luck, lol. Looks like I ran into two more issues when using the current Zero Project patch alongside the MSU-1 patch (the regular version of the MSU-1 patch this time, though; the Zero "Weapon Get" screen graphic bug didn't appear again, thankfully).
1.) When fighting Volt Catfish as Zero while using the Tornado Fang weapon, the ammo counter rolled back over to full instead of remaining empty after I had used all my ammo. When this happened, the in-game ammo bar looked a little strange, too (dunno how to properly describe it other than it looking glitched or corrupted). The bar then remained full when in-game, but on the pause menu, the ammo bar accurately reported how much ammo was left since the bar refilled itself. After defeating Volt Catfish, the ammo bar functionality resumed functioning properly...from what I could tell, anyway.
2.) I was not able to enter the boss room in Gravity Beetle's stage. Period. I'm not sure if it's because I switched from Zero to X after entering the hallway leading to the room or what. The door just wouldn't open, so I had to hard reset.
I hate to bring this up again since you explicitly stated you had no interest in MSU-1 functionality, but I cannot tell if these issues are appearing because of my use of the two patches at the same time, if it is because of something going on with the current Zero Project patch, or if it's the emulator I am using (the SNES9X core in RetroArch, mostly because of how easy it use to use MSU-1 stuff with it). Variables are the worst when trying to debug things.
EDIT: Also looks like the PCM file for Neon Tiger doesn't play when using the MSU-1 patch in tandem with the Zero Project patch. Hmm.