Thanks to a very helpful Apple representative, we were able to determine that the problem for my situation was with an export plug-in.

This drove me nuts until I found this thread: http://discussions.apple.com/thread.jspa?threadID=1715124

User/Library/Application Support/Aperture/Plug-Ins/Export <- move contents of that to another location, and try creating a Vault. It worked for me. Now my Aperture library can be excluded from the dumber Time Machine backup, saving lots of time. Aperture Vault backups take only the new stuff, not my whole library.