In case it helps anyone else, I contacted support and got this resolved. Basically, settings the first DNS server as the internal DNS created a static route through the primary WAN connection. When the fail-over was using the secondary WAN connection, it couldn't contact the internal DNS server since the static router was through WAN1. Removing that entry and having it use the "domain overrides" seemed to fix the problem. I'll be testing early tomorrow before the users show up.