Made another too-long comment on YouTube and it'd be a waste to let it disappear into the ether so here it is:
I still want to play the PSP version the most, if only for those extra characters and classes, but it needs all sorts of hacks for a comfortable experience.
Slowdown: Fixed with LivePatch or a patched ISO.
Graphics: Fixed with LivePatch or a patched ISO, and probably combined or bundled with the slowdown patch. Makes the game look absolutely perfect on PSTV with Sharpscale, or on original hardware with component output with a RetroTINK 4K zooming in. Many PSP games actually have "pixel perfect" screen modes that shrink the game area to 240p for extra sharpness; such modes are too small for me to bother with on an actual PSP screen, but benefit tremendously when playing on a TV.
Soft Reset: Best plugin I've found for this is GameMenu, also known as In game VSH menu (satellite). Highly configurable so you can even hit that musical note button on your PSP to bring up a menu in-game where you can reset, but I like binding it to Home + Select so I can reset with a Dual Shock 3 when playing on a docked PSPgo. There was another plugin called EzGameReset but it tended to crash the game back to the XMB instead of resetting.
Spell quote restoration: Need a tool called Valhalla, but I don't think there was much progress made on this and I haven't bothered with it. Hopefully someone out there documented all the Ivalice Chronicles spell quotes so they can be easily implemented.
Music restoration: Practically modern-day sorcery and I have yet to attempt this. Ideally you'd use the Final Fantasy Tactics OST rip. Then you'd have to do the hard work in Audacity with finding and marking beginning and end loop markers for each track, encoding to .at3 with AT9&AT3 Converter, then putting it all together with UMDGen. At least I think that's how it works. When I've solved all my other problems, have all the free time in the world, and am bored of absolutely everything else, I suppose I'll try this for real.