Got it done. It required a transformer to go from 240 volts to 24 volts; I used
this one.
The Nest will turn on with two wires or three, but to actually get the heat to turn on you need to use C, W, and R. Paid a friend who does HVAC for a living to solve that problem for me.
The steps were:
0. Turn off power to the unit. I have two breakers, one for the white wire and one for the black.
1. Get old switch box holding old thermostat out of the wall. It was a new work box, so it was nailed to the stud before installation. I got out a little drywall around it and then used a hammer and chisel to take off the tabs holding the box to the nail so I wouldn't have to make a giant hole in the drywall.
2. Attach transformer to the new junction box using the supplied nut that fits into a 1/2-inch knockout. I then threaded the thermostat wire from the transformer back into the box
3. Bring in all the wires - three sets of white and black, one coming from the breaker box, the other two going to the baseboards - into the new metal box.
4. Put the metal box in the wall. It had some small holes in the side that I put nails through to attach it to the stud. The old nails that held up the old box I just hammered out of the way. The transformer fit behind the drywall so with a little persuasion I got everything in there.
5. Attach wires: all the whites connected to the transformer's blue wire, the black from the breaker connected to the black from the transformer, and the blacks to the heaters connected to the red on the transformer.
6. Wire up the thermostat, put it on the wall, and turn the breakers back on. It works!
Note that when you have two Nests in the same house the app wants to link them for auto-away purposes, which is the exact opposite of what I wanted. So, I had to set them up as separate houses in the app.
