Same situation for us in Central Texas. I wonder if a power generator could run the electricity needed for the blower and electronics in a HVAC unit.
It is doable, but difficult.
I installed gas logs in March and will use that for heat next time ERCOT decided to cut our power off.
A 2000 watt gen set can run your gas furnace igniter and blower.
You need a substantially bigger one for central A/C.