I probably wouldn't believe him either. Google should have an option to revert to the last trusted config after some verification method. Google support is bad, I'll give him that.
All this to avoid roaming charges? And then refusing to share a personal email in this scenario and missing meetings because of that.
I'd argue that changing the MX to fastmail or Microsoft would be much faster than a postfix+dovecot solution on a VPS but I think he's just refusing any solution based on his principals.