SOLVED! (I hope)

I started to realize, after trying various physical tricks with the thermocouple wiring (at the motherboard connection and where it comes out of the heating block), that the temperature decline started to happen precisely when the "active cooling fan" (the big centrifugal one on the side of the extruder) came on during the print. So I tried another print with "Use Active Cooling" unchecked in the MakerBot Desktop settings. After killing that fan, the extruder temperature stays within 1 degree C of the target. If necessary to get good PLA prints, I may try to re-enable the fan, but set the maximum power level down below the 50% default.

Any suggestions from expert users why the active cooling would drop the temperature so much? Is it possible that the thermocouple is getting cooled by the fan and not giving accurate readings of the actual extruder temperature?