Having the default status as Failure will actually work the way you're looking for. You create rules for the Success and Warning emails, and then any email that doesn't match the success or warning criteria will be marked as a failure. So that would include emails with the text Failure, or anything else that's not part of your success/warning criteria.

The overdue failures are a separate mechanism that mark the check as failed when an email is absent.

Hope that makes sense, please let us know if you still have any questions

Thanks!