Sorry for the slow response; garage time has been hard to come by recently. I did test the vacuum at the recirc door, and it's getting enough suction.
I finally gave in and pulled the whole HVAC box out so I could see what was going on. Based on the sounds they're making, the actuators are all incredibly corroded on the inside, which means they will slowly move under vacuum (except the defrost vent, which was completely stuck half-closed), but they won't return to their resting position once it's removed, i.e., they're all half-open all the time.
I bought a salvage HVAC box to use for parts, along with a new heater core, since I'm already in there. Between those, and some time cleaning and de-clogging everything, I should be able to get it running smoothly. I'll post if I run into anything else, but I expect this will do it.
Thanks for all your help running this thing down, guys; I really appreciate it.