affordable 2000w inverter

I find the voltage sag under a load is the same for any SOC. It is the amps that does it. So if you get 0.7v sag at 80% SOC, you should see 0.7 at 50%. If your inverter alarms at 11v, you can start at 12.1v (50%) and it will drop to 11.4 and then go down slowly from there the longer the thing runs. Having more AH in the bank also helps with how long it takes to get from 11.4 to 11.0.

If the furnace happens to come on just then, that could do it though. At least the inverter will keep running to 10.5 and just alarm at first, so you can finish making your toast.