Okay, so I actually solved the issue. When you install the Reunion mod pack, you launch it through the regular ffvii.exe. The problem was that the reunion installer was installing to ffvii_en.exe, since I have the steam version. Since you have to convert your steam version to the 1998 version in order to use 7th Heaven, you can't launch with ffvii_en.exe anymore, so I had to delete it and then run the Reunion installer again.
Then I ran into another issue, where 7th Heaven was using a folder called "textures" as its modpath. Reunion points the game to a folder called "reunion" instead, and ffvii can't have two modpaths. I fixed this by changing the modpath in 7th Heaven to "Reunion" and then reinstalling the reunion pack. Now everything works, and I can use 7th Heaven and Reunion at the same time. I just point 7th Heaven at the regular ffvii.exe and launch through 7th Heaven.
I didn't see this fix anywhere else on this forum, so if anyone else is having this issue, this is how to deal with it.