And I was thinking the same thing. If the bath is not huge and you can close the door, I suspect it would maintain 45 degrees without a lot of run time(depends on many things). 45 degrees is a lot easier to achieve and maintain than say 65. The question is the bath your talking about, is it in the core of the house or located outside of it?
I have a situation with a bath and kitchenette in an area of the house we don't usually heat in winter. It stays above freezing with some solar and ample insulation, but the last few cold spells had one supply pipe freeze. No damage, but I don't want to chance that(water). So I'm devising an installation of one of these for protection. I wish I could go back to the design stage of that,...
You have a great set up with the Monitor and fireplace. Both the appliances have 100% distribution efficiency. Sadly, too many houses I see have no option to heat that way. I'm aghast at the amount of fuel some of my friends use to heat their homes around here(and they're usually cold!).
We have a third floor with 2 bedrooms and bath which we close off now that the kids are gone. Closing the 3 doors cuts off a large cube of space. It's in those bedrooms I'm now installing these heaters, but I'll leave the breakers OFF. Those rooms never go below freezing because they're over the core of the house. The bath on the other hand is centered in the heated core and won't go below freezing.
Tough choice you're facing. It's ridiculous to heat the whole space simply to keep pipes from freezing. Hope you find the best solution.