I did just realize that I could solve this by just directly connecting the 12V PSU to the 12V physical relay. That would be simple, but it would also mean that if the SSR controlling my 12V PSU were to fail closed it would close the relay contact and put power on the contacts for the SSR controlling the heated bed. It's highly unlikely they would fail at the same time, but I'd like to find a solution where the SSR controlling the bed heater can only get power on its contacts if the Duet thinks the printer should be on.