It's been a looong time now, but having had about 17 of the 64 Plymouths, I used to have recurring problems, and the control valve was on that list.

Drain it down, or just wire the hoses to hang above heater level, vise grip, etc.

IIRC, removing the radio first may have eased clearance problems, but for the most part it is a pretty easy job, once into it you will have it out in short order.

I'm with the other guys on the shutoff, My take on it is that it was being used to control flow thru the core, as a shutoff in one line won't stop coolant from occupying the core, so the valve probably isn't (wasn't) leaking either.

And, may I say, that is a great looking engine compartment, most of mine were much worse, (and much newer!) back in the day ... color is the same as VT state police used, had a few of those too.