....what your not satisified with the problems you already have, and you want to add more?
Does the 8bit test say Pass or Fail?
If it says pass, and if ATI's 8 bit pallet is 100% correct, you can use the FF7config.exe from the TNT patch (don't check the Riva option), and give that a go.
If you get grid lines, or missing backgrounds....then your going to have to figure a way to disable the 8 bit pallet from the ATI driver, and that I don't know how to do.....if it was a Geforce, I would tell you to use Rivatuner, but Rivatuner isn't going to work with ATI. You'll have to find a third party ATI video driver tweaker on your own, if one even exists.
If you ever do find a way to disable the 8 bit pallet, then you use the FF7.exe and FF7config.exe from the TNT patch and "check the Riva option". The FF7.exe from the TNT patch will only work when the 8 bit pallet says, FAIL; and you can only use the FF7.exe from the TNT patch with the RIVA options checked.