The best thing is to probably never turn it off, but if that is not possible (e.g., you only want to run it when the sun is shining), then when you first turn it on you simply have the thermostat set a little low (at current house temperature, perhaps), and gradually raise the thermostat over the course of a couple of hours. If you had a power monitoring system installed in your circuit board panel (e.g., something like Sense) then you could see what the wattage draw is for the breaker that feeds your minisplit and act appropriately with the thermostat. Also, most of these mini-splits have a short-term "Powerful" mode to provide a burst of extra heat for maybe a half hour or so, and the max input power ratings might also be based on that mode.
I think you definitely want to consider three things when you look at what mini-split you would install:
- What the modulating range is - getting something that can operate over a wide range (e.g., 10 or 20 % on lowest setting vs. 30 or 40% on lowest setting) is better so that you unit operates more in "low and slow and efficient" mode. The cheapest units usually have a narrower modulating range.
- Not chasing low-temperature performance as much. Extra low-temperature units will provide heat and/or more heat at very low temperatures (-17 degrees F, -25 degrees F, etc.) but their efficiencies are not as high when temperatures are warmer (which is most of the heating season). They also cost more. What you really want is best efficiency in the temperature ranges you think you'll be using it in. I think I remember that you have two woodstoves in your house, so you don't need the minisplit to help out when it is really cold.
- Maybe going one size higher (15 kBTU) IF the modulating range goes pretty low (down to 10%, let's say). The max input power requirements are probably not that much more and the cost difference might be minimal, but the unit will be operating low and slow more often and therefore in a highly efficient mode more often while still meeting your heat requirements. Essentially, it will use less electricity (probably) for a 15 kBTU to deliver 12 kBTUs to your house than a 12 kBTU unit to deliver 12 kBTUs to your house. Again, this all depends on the particular manufacturer and their particular model - you need to get the detailed performance curves like I attached earlier for my unit.
BTW, been meaning to tell you that the rebuild of the Woodstock stove really came out nice - very nice work!