Ok, a year later...I've got two different solutions in place for comparison.
First up, the wooden solution I had planned out (well, almost - it has 2x the bolts and washers of my original design for stability). Works well, easy to make sure the bolts go eactly where they need to through the HWC, it's sturdy, easy to install, and predator proof...just kinda ugly. I opted for wood on the inside to keep sharp HWC bits away from the chickens.
And then, on a different coop, a recessed male outlet I just installed this afternoon on the run of my other coop. This required a bigger hole in the HWC than the wooden solution did, but for this coop my placement options were pretty limited and I actually kind of needed the extra cord length this provided on the inside.
I was originally not sure I wanted the cord connection happening inside the chicken area, but I now have some weatherproof cord connection protector that are
very stiff to open even for me, so no chicken is going to be strong enough to open it. When not in use, I will need to cover the female end with something to protect it from dirt/mosture and perhaps should tie it up out of reach. I probably also need a piece of wood around this for better stability when putting in or removing the extension cord, but it's on there pretty good as-is.
There are some other square-plate similar recessed outlets that might have been easier to install with more room for washers without needing a wooden plate. I liked the compactness of this one though and the fact that I could rotate the flap cover independently of the rest of the outlet.
The heated water bases are pretty low power consumption. Both are currently going into one of these outdoor-safe wifi controllers. I have them programmed to turn off after the chickens are roosting and turn on again about an hour before auto-doors open. That gives time to get the water thawed.