I've done some digging and found the source of bloat (not sure why the App directory is missing a name). I don't know what these files are yet, but the largest I've seen is about 60MB's, but I have 395 of these averaging about 6MBs each. I have not taken any photos that come close to 20MBs and don't have video transfers enabled. The directory name is the MAC address of my previous EyeFi Card. I feel safe in deleting the directory but I feel like I'd mess up the SQLite DB (or w/e this DB structure is). I'll muck around some more and see if I can find the contents of at least one of the files.
Odd thing, the directory for my current card only has one of these files from 01/09/12. I know I've done some iOS to Computer transfers with this prior to that date, so maybe the bug got squashed in an app update.