I ran into this and eventually found the admin utility for moving attachments out of the database. Currently there are bugs open about errors for orphaned and missing attachments (see 0005837 and any dupes), which would be a great place to tell people that an admin utility exists.

While the patch discussed here is attractive in that things "just work", it seems like a lot of novice admins might never discover the moving utility. Not sure when it would be appropriate to have the system suggest this to an administrator if the patch is applied.