Thanks for the suggestion. In my OP, I mentioned that we had already replaced the water pump and thermostat. Back in March, after I posted, I went in to change the timing belt and the leaking radiator, so while I was in there I re-replaced the water pump and the thermostat. I burped it bery carefully with teh front end way up and the engine revved high. A lot of air came out.
Sadly, though, it still doesn't heat.

I keep hearing about the "blend door." I guess I'll look at it next, prolly when it gets cold out again. I have my doubts that that is the problem, though, as the hoses to the heater core don't seem to be hot enough.

We are still completely baffled.