A final thought occurred to me: even though the EDS was not forwarding incoming mail, it was still accepting the incoming messages. Consequently, a secondary MX record wouldn't have even come into play because, as far as external SMTP servers were concerened, there was no outage.
There could be a setting whereby, in case of "Degraded Performance" the connection is rejected in such a way that external SMTP servers are forced to go to secondary MXs. How that would work is a question for somebody smarter that me, though. Or, there could be a web-based interface (similar to the quarantine) where incoming queued messages could be reviewed. That's a nice solution. Have a nice (uptime-filled) weekend.