You will likely be disappointed in cellular availability during a long blackout. I'm in the Midwest in a metro area of ~200k. We had a major weather event which took out power for 1-2 weeks. Almost all cellular towers went offline as soon as their batteries died. It seemed there were only 1-2 towers in the entire area that had generator backups.

Have you considered any of the solar “generators”? Basically they incorporate a solar controller, inverter, and battery into one easy to use package. I typically get at least one outage/year here in the Midwest. I bought a kill-a-watt to measure what my fridge is using (about 2kwh/day) and it looks like one of these devices could keep that running through a longer outage. If you want to go even further you can buy more batteries!