I guess this was ignored, which is sad.
I found out about Project Diva from the PSP games as well and can't play without using the Directional Pad too, so I just gave up on the High Scores and just played for fun.
However, I do know of a way to "kind of" band-aid fix this but haven't done because I'm too lazy.
Try using AutoHotkey and program it to have it ALSO press the buttons you have for Triangle, Cross, Square and Circle when you press the buttons you have for the Directional Pad. This way, the game will recognize you pressing only the Triangle, Cross, Square and Circle buttons when you press the Directional Pad.
In theory, this will work but it might have problems with swipe notes facing the same side, because you're pressing the same key at the same time.