Yes there is a solution... Sorta.
After applying the Hi-Res patch, apply the cetra 'windowed mode' patch to the ff7.exe. Just make sure you have your res set higher than 1280x960 on the desktop. That should work.
*edit*
Unfortunately with this fix, the movies have two big black bars running down them, but I think thats the cetra patchs fault. Thats how I got it working on my widescreen laptop, since I would normally have the bottom cut off.