There's a LOT of good things to look into here, thanks everyone!
Suggestion 1: The Pro 2 controller had been working so flawlessly until now that I honestly stopped thinking about controller firmware. I used 8BitDo's official update tool, and found the controller was like 4 or 5 versions behind current, so I updated it.
Suggestion 2: Again, my Pro 2 controller's A-Input (Android) setting just always worked from the get-go with no issues for me that I never bothered changing it. It was also the convenience factor that I was already using the X-Input for quick pairing to my Steam Deck. However, I do know the mass improvement between the outdated D-Input and the much better X-Input. I've switched it over to X-Input for the MiSTer, this is my favourite system out of anything I use the controller for, it deserves the quick pairing regardless.
Regarding the fuses, it sounds like the power adapter is the one to possibly look at. I actually purchased a premade set from a seller online, who provided their own power adapter (not sure of its output, but estimating from brick size, I'd guess around 15-20 watts). Honestly, after the first occurrence of the fuse blowing, I wondered about the power supply and switched to an old official Apple USB 10w adapter with a USB-C to USB-A cable. If low output is a concern, I think I also have a larger wattage adapter I could try.
Anyways, so far on the controller front, it absolutely did pair a heck of a lot quicker than it's recently been taking pre-update and when I was using the A-Input (I honestly don't know how Android input protocol compares). If anything changes there, I'll definitely report back, maybe it'll help others who come across it.
I think I'll need to get some more confirmation on the fuses part. My original MiSTer seller is very nice and sent over a pile of fuses to help troubleshoot the first time, and that's how I found out the fix. However, he lives overseas, so it takes a while and it'll eventually start costing pockets of money to buy these fuses if it just keeps happening. Hoping to nip the problem in the bud before that even has to be considered. I think I'll start by trying a slightly larger wattage power adapter from a reliable company, but if anyone does have any other input/experience on this, I'd love the notice!
Thanks again everyone! Super helpful stuff.
[Addendum] After pairing the controller using X-Input and with the firmware updated, it's still exhibiting issues. I'm finding the controller still doesn't respond for several seconds on some occasions, and even sometimes, I press something like D-Pad Down one single time, and a second or two later, the UI moves down like 10-15 times in rapid succession. This seems to happen much less in game, but it does happen on the OSD more. This is all still really weird to me overall, I used the MiSTer and this exact controller for well over a year in this same configuration with no issues. It's just now that it's being really finicky.