My impression was that most typical inverters used in home PV installations have (required) anti-islanding safety features where they only output power if the input waveform (from the grid) looks good. It seems like manually islanding the home at the breaker would just look like an outage to an anti-islanding inverter and it would still shut down, so wouldn’t you also need an inverter with a manual switch to disable anti-islanding? Or how would the anti-islanding inverter detect that the home has been manually disconnected from the grid?
Yes, it's theoretically possible to grid form with an inverter and battery to trick your solar inverters to thinking that there's a compliant grid to island your house, but doing so safely is not for the average end-user, and may also involve dangerous components like suicide cords.
Related reading: https://en.wikipedia.org/wiki/Islanding, https://en.wikipedia.org/wiki/Grid-tie_inverter
Ohh, scary!
Desperate times call for desperate measures. How to use a "suicide cable" safely.
1) Make sure the cable is built properly (not cross wired)
2) Disconnect from the grid using the main breaker outside the house near the electrical meter.
3) Plug the cable into the house wiring first so energized contacts are never exposed. Preferably in a location not easily accessible by children or idiots. I typically use the outlet in the ceiling of the garage normally used by the garage door opener. I tie the cable to the door opener mount so you can't disconnect it just by yanking on it.
4) Plug the other end into the inverter or generator
Enjoy a cold beer while watching TV waiting for the grid to be restored.