Ok, just a follow up. Nest did replace the thermostat, so good on them. I added several ferrite beads and a torroid wound with 10 turns that I placed in the furnace. This was directly on the thermostat control wire. I haven't had any issues since on any band. Problem solved. I am fairly sure that the issue was linked to the bands that were being operated on, as well as the total length of the thermostat wire. The length in my house was likely tuned to the 80 meter band, and generated some common mode current on the thermostat wire that the solid state transistors in the power control ring of the nest thermostat could not withstand. There is a possibility that not everyone will have the same issue, but why risk it. If you have a smart thermostat, toss a couple of chokes on the control line to ensure it's continued operation.