I'm using the original 'fat' PSP and it has not been modified. The game comes with the firmware update of 3.80 or 3.82 (I forget which one, but I think it's the latter) to run it.
You should know by now that I don't modify my systems, Geo!
The load times are fairly bad, but you also get used to them. Like I said, the animations can be turned off which helps. Those trigger a 5 to 6 second pause if you leave them active, repeated a few times per turn on the busier maps (you can set them to appear randomly, all the time or not at all).
When enemies move, you're sometimes waiting around 35 to 40 seconds for later maps. Earlier ones with fewer adversaries aren't as bad, it didn't seem like. As you clear off enemies toward the end of a given battle, things improve a lot.
All of that stuff doesn't stop it from being a really good game that I think a lot of people will enjoy if they give it a chance, but I didn't feel good about scoring the game any higher because those issues never fade away entirely (plus as noted, the story really is presented poorly).
"Too often we enjoy the comfort of opinion without the discomfort of thought." - John F. Kennedy on reality
"What if everything you see is more than what you see--the person next to you is a warrior and the space that appears empty is a secret door to another world? What if something appears that shouldn't? You either dismiss it, or you accept that there is much more to the world than you think. Perhaps it really is a doorway, and if you choose to go inside, you'll find many unexpected things." - Shigeru Miyamoto on secret doors to another world