Just a follow-up.
I initially removed the HCV cable, lubricated it with liquid graphite, and reinstalled. When I lubed it outside the car, it seemed much better. But, when installed, routed in the 180 deg arc, and pinched by the spring clips, it was really stiff and didn't work.
So, I bought a new Toyota brand one (in fact, that's the only place I could find one). Anyway, it slides quite easily. After install, you can move it with light finger force. And... this totally fixed my HVAC issue. Now, the blend doors reposition properly, and the heater control valve is moved properly.