Bringing my own thread back from the dead.
Still own the Model 77 Fluke discussed above. And it's been displaying the same issue with the resistance, though now it's bad enough that it doesn't measure accurately at all. I opened it up and reflowed the solder on the input jacks, but no change. So I checked R1, the fusible resistor (tests ok), and RT1, the 1.1k PTC thermistor. My understanding is that this should measure 1.1k ohms at 25 degrees C, which is just a bit warmer than room temp. I'm measuring 0 ohms. Wouldn't this measure open if it had failed?