Ok, I plugged the HTC-supplied TP2 cable into the same (front) USB port that has always worked for my Fuze, and which still works fine for my Zune, and I only got a 1/4 charge overnight! Went from 23 to 45%.
However, the computer was in standby the whole time. Does the USB port deliver even less juice in standby than when the computer is running? It is strange to me that I am only discovering this limitation with the TP2 and never had any issues before.
Well, if I want to charge and sync without unplugging cables, it looks like I need to get a powered USB hub.