Hi, Brian,
What you're seeing looks like it's related to a known (but up until recently rarely manifesting) issue with OpenID, the authentication method used for the old Google Apps integration. The problem is actually unrelated to the new Google Apps integration or to the upgrade process and isn't connected to the September 30th deadline for migration.
However, migrating your domain to the new Google Apps will solve this issue, because the new integration uses a completely different method of authentication (OAuth, rather than OpenID).
If you need any further help with the migration, please let us know.
Best,
Elizabeth