This is a little frustrating. The latest driver release "wme-j5-30-1-b02.exe" is actually the most feature complete, looks great, and renders 3DMark 99 correctly. Paletted textures seems to be broken though, and I think that this is what is causing D3D rendering with FF7 to fail.
The earlier driver version "w98_rxl_4_12_2647.exe" fixes paletted textures and FF7 works great, but there are rendering errors with 3DMark 99.
I narrowed the problem down to two files:
ATID32AE.DLL (ATI Rage Pro DirectDraw HAL)
ATI3DRAE.DLL (ATI Rage Pro Direct3D HAL)
If I install the latest driver version but overwrite these two files from the older version, I can be on the "latest" driver version but have FF7 work. Of course, this also rolls back the other fixes and 3DMark 99 has errors.
I tried replacing one file at a time as well. Copying just ATI3DRAE.DLL (D3D HAL) allows FF7 to pass the paletted textures check, but the game crashes when it's started; so ATID32AE.DLL (DD HAL) is required. I tried using the new D3D HAL with only the old DD HAL, but then the FF7 config program crashes, as does every other D3D program I try to run.
I looks like both files need to be updated in tandem; the DD HAL and the D3D HAL. The latest one renders more accurately while the older one has some render problems but has paletted texture support.
I wasn't able to locate any other driver release between these two versions to compare. Since I only notice the rendering error from the old driver in 3DMark 99, it might not be apparent or applicable to games. The older driver seems to be the best and obvious choice.