Well, I found a fix by getting a custom midi driver, having FF7 use that and then muting it. Was up on some gamespot forum post:
Download Loopbe1 and install it. Once it is installed, go into the configuration-Midi of FF7, and change the Midi Driver to LoopBe Internal Midi. Then, on the taskbar right beside your clock, there should be an icon for LoopBe1. Right click it, and choose "Mute".
That should work.