I figured out real quick-like that removing them all the way would be disastrous. Thanks for that tip though.
Also- I think I have a good theory as to why the heater unit would not budge …
I gave the task of installing a new wiring harness to a guy who does such things for a living. (I lack the patience for that job.) In the course of that work I gave him the heater unit I had rebuilt and asked him to install it while he had the truck. It dawned on me today that I didn’t research or acquire a gasket kit ; it didn’t occur to me at the time. (The guy fabricated a rather nice fan motor hole cover for the firewall.) I think he used a squeeze tube gasket product for the interface between the unit and the kick panel - my heater is glued on.

That would explain my frustrating experience of today.