Well Aali's driver helps a lot lot lot with this and also makes the game look way better and lets you use some of the best mods made for the game. It's literally THE must-have mod for FFVII.
I'd also recommend
LoopBe. Install it and set it as the midi device FF7music uses. It's a midi that creates no output so it mutes the game's midi output so nothing can get in the way of FF7music.
Also, which midi.lgp did you delete? I think FFVII might use one of the files in the music folder but don't quote me on that. If you use LoopBe you shouldn't have to delete any lgps. I'd suggest replaying that file and trying loopbe.