So crisis is over, thread is a little old now, but just showed up on an email to me, so I'm throwing out a possible solution for someone in the future. I have all my computers and TVs plugged into small battery UPS devices. When the power goes out, the UPS sounds an alarm and immediately switches over to battery. When the power is restored, the UPS switches back to mains, shuts off the alarm, and recharges the battery.
Even my smallest $40 UPS at 450 watts will run a computer system for about 20 minutes. That might not sound like much time, but it's more than enough for the computer to shut itself down properly if the power is not restored in 15 minutes. But computers are constantly running and sucking up electricity at a steady rate of about 400 watts.
How many watts is your incubator? I imagine there is a thermostat that turns on and off depending on the temp. Does the incubator draw any current when not heating? I would think that the heater is off most of the time if the incubator is well insulated. Maybe throw a blanket around the incubator just to help it if you needed more time. At any rate, I would think that even a small battery UPS could provide power to an egg incubator for what, hours? If you spend more money, you can buy larger battery UPS devices and increase your downtime protection. And yes, you can hack the UPS to use a car battery/batteries for almost unlimited running time (search YouTube videos).
I plan to incubate eggs someday and I will be plugging my incubator into a UPS, not so much for long term storm outage, but more probable is that my attached garage GFCI outlet trips and shuts off the power in the garage but the rest of the house is unaffected. I want an alarm on that power source, and if not home, want the battery backup feature of the UPS to kick in until I get home and reset the GFCI circuit.
Hope that UPS idea may help someone.