What I'm most worried about is not having the heaters turned up high enough when I'm away and the temperature drops. I think it would be easy for me to get the house nice and toasty with the wood stove, dial down the heaters accordingly, and then forget to dial them back up before I leave. I do have remote temperature reporting setup now, so basically I just want a lifeline when I'm away so that I can turn on some heat in the house if/when I get a notification that it's too cold. To do that, I probably only really need to rig up one or two heaters (not all 10.) Ideally, I would do it to all of them, but it sounds like this is getting expensive fast -- I think I could relegate one of the heaters to be that emergency heater that I don't touch the thermostat on and normally leave the power turned off. Then, if I get an emergency low temperature alert, I can kick that one heater into action. The house is basically one big open space, so heat will travel fairly well, at least enough to not let pipes freeze.
So, I think I'll start with automating just one heater and go from there. Since the heater wouldn't be turning on/off all the time, I think it would probably be safe to just wire it up to control the power to the whole heater.