Think we found it. Old heat pumps are horribly inefficient. Personally, I'd have to think hard about replacing it with ground source, though. While very efficient, the capital cost of a well or buried loops often makes the payback many years longer than just buying air source heat pumps. You almost certainly have ducting as well, and most leak like sieves.Just one 5 ton heat pump that is showing its age...
I live in Maine, so we know cold. None of the three buildings with heat pumps have backup strips, and all provide heat at below zero. I also track use with Emporia Vues in all main buildings. It was 8F here this morning, and our buildings were all toasty. At no time has the heat pump in the building I'm in exceeded 3.56 KW this morning, and that happened for about 2 minutes, in a defrost cycle.It was under 2 KW for the vast amount of this chilly morning I just checked this months peak 15 min demand for the heat pump in our home and it was 1.73 KW.
So, I'd start with a heat pump changeout, and strongly consider multiple units over a ducted system if those ducts can't be sealed. I might also consider some automation that temporarily suspends charging your EV when demand begins to exceed some threshold (e.g., a relay controlled by inexpensive home automation, communicating with the Emporia Vue. Personally I use Hubitat but not for the purpose I just described (no EV). Bottomline: Addressing this first with batteries seems like an expensive route. I'd try improved efficiency, starting with that old heat pump, first.