Thanks for the additional information, Brian. I did some testing with my infrared thermometer--which I just remembered that I have-- and found some interesting data:

Around the heater valve, the hoses all were around 150 F.

With the air on for about ten minutes, the vents read:

driver left: 50 F, middle left: 64 F, middle right: 78, far right: 79

The last two are about the same as the outside temperature.

So now I'm starting to question whether my problem is the heater valve.