In the process of setting up my new install, I unpacked the meshes BSA, pyffied everything, and repacked it. It's named Oblivion - Meshes.bsa, just like the original one... but the game won't start with it active. If I rename the original one and use it, the game works fine... except I'm missing a crapton of meshes. I could try reinstalling the game again (since I can't simply install it on another drive and copy the BSA over), but I'd rather try to find a solution that lets me use the new BSA. So... any ideas?

The name should not include the file extension. Simply "Oblivion - Meshes". Did you adjust the file paths/tree when you made the new BSA? Also when repacking the BSA, make sure you set 'no file compression'. As an aside, this is why you should always make a copy before adjusting any files, if you have the space for it.