Thank you so much for looking into that music issue! I'm seriously stoked that it's being recognized and addressed. Cloud's revelation is my favorite scene in the game and I could never get into the PC version solely because that scene was off (I'm picky, I know).
I'd like to address other music issues between the PC and PSX release here:
1. "Turk's Theme" quits playing during the scene where Reno walks over the flowers in Aerith's church. In the PSX version, it plays continually without any interruptions.
2. "Who are you?" is replaced by "Infiltrating Shinra" when Cloud sees Jenova in the Shinra Headquarters. "Who are you?" plays briefly when Cloud is looking into the chamber, but then immediately quits once he falls over. In the PSX version, it played until Cloud, Barret, and Tifa were done talking.
3. "Those Chosen by the Planet" is replaced by "Under the Rotting Pizza" when Cloud runs into the mako reactor during the Nibelheim flashback. Having "Under the Rotting Pizza" interrupt it seriously messes with the mood between the scenes.
4. Opening a chest in the Cargo Ship causes the sound effect of the ship's motor to stop playing.
I was able to fix issue 1, 2, 3 by simply editing the game's script with Makou Reactor. If you're interested I can post the solutions here, but they aren't particularity interesting. Most can be solved by simply moving the line that calls for the music to play.