Huzzah! After uninstalling and re-installing Pro-C on my PSP the game is working perfectly fine. It's a clunky piece of junk with a loose battery and jammed buttons but it'll do for now. Two of the reasons I got a Vita was PSP emulation and "easy access" to games so it's a shame I couldn't get it working, if only we could pinpoint what exactly stop it form working on the Vita... I read on r/Gundam someone has the same issue I do but he had it on the PSP. I think in the end, it does have something to do with the Vita's current PSP CFW. Not sure what can be done about that.
Edit: At Crashman's suggestion, I tinkered around with the Adrenaline Firmware present inside of the PSP mode of the Vita, I found out to my surprise that it is actually a re-named Pro-C! Without even editing anything I was able to explore the GUI and make minor changes (nothing special, you can do this in PRO-CFW easily) So now things get even more curious! I will test a vanilla piece iso of Overworld and see if that's any different.