Based on that post, is it possible the Google Drive API is interpreting multiple requests from UpdraftPlus (within the same Google account) as being from the same app (even if the client ID is different) as somehow being different and thus exceeding the credential limit in some way.
In other words, the solution may simply be to create a different Google account for each site? Or just explore using SFTP since the fix may not be easy, even if we can collectively determine the root cause?
Interestingly enough, we've only been using UpdraftPlus since ~June 2013, so that post wouldn't seem to apply, and our initial site using it hasn't ever generated an expired oauth session and it uses the same google account as the other 4-5 sites.