Sorry to bump such an old topic, but a kind individual named Canzah made such a patch in 2014. Shin Megami Tensei: Persona sadly eviscerated at least 1/3 of Revelations: Persona's music, so a direct 1:1 music reversion patch isn't possible.
The opening song, Dream of Butterfly, is the only new song that remains from SMT: Persona. The rest are from Revelations: Persona.Grab it here!
It's an XDELTA patch; XDELTA UI is included. Here's what Canzah themselves had to say about this:
Mind you I never went to officially released the patch officially since I'm not happy with how it is.
First of all, I could only replace existing P1P tracks with P1 PSX tracks. That means I was only able to include roughly 1/3 of the music that was in the PSX version.
Secondly, I had to shorten some tracks due to filesize protection that the game uses.
If you're still interested however, then here you go:
[Mega link that could potentially go down]
Personally I'd instead just recommend playing PSP version first and then replaying the PSX version already knowing the plot and using online guide for item translations since that way you will be able to experience original music properly and not in a shortened/cut down form.
You're free to distribute the patch if you so desire, I only ask that you credit me as the author if you do so.
To anyone who is viewing this topic years from now and if, for some reason, the Ze Bucket link is down, contact me via PM. I'll likely keep this little beauty forever.