Well, it wasn't the water pump... but I have heat!
My one-year-old serpentine belt was the culprit. As I was replacing the water pump I discovered that the belt was dry-rotted, cracked, and starting to split lengthwise along one of its grooves. Before anyone doubts this being the source of my troubles, hear me out.
I took off the old water pump and decided to take off the back plate to see if the theory that the impeller was rotted away held up. Nope, the impeller was a bit rusty but fully intact and the pump spun easily without any play. The pump wasn't expensive, so I don't mind all that much that I've replaced it - but it wasn't the culprit.
I didn't notice the condition of the belt until I went to re-install it, at that point the new pump was already in place. So, I borrowed a car and went to get a new belt. Upon installing the new belt, I noted that the tensioner was in a dramatically different place than it had been with the old belt. Obviously, the belt had been slipping on the water pump pulley enough that the flow was not sufficient to drive coolant through the heater core in its installed position. So the theory that the pump wasn't pushing enough coolant was correct - just not for the reason we all thought.
I never suspected the belt as it was replaced when I first got the Tahoe - but it was completely shot.
Who knew?
Took a good look at the power steering pump and decided that replacing it was a job for another day. Looks to be a giant hassle of a job. Had I started, I would have been there until midnight.