Assuming you have enough solar, how about running your 5+ ton HVAC system only when there is enough production? And properly insulating your home, of course, using it as a thermal battery of sorts.
If there is a grid outage, surely one can shift consumption to solar production hours while using the battery for the always-on systems (fridge, lights, some computing...).
Insulation won’t help post-hurricane when they are trying to fight humidity/latent heat. Your thermal battery comment makes it sound like you are viewing this from a cold stress perspective (in which case a tight, highly insulated home is indeed a great way to slow heat loss and keep the home warm), but they are talking about dehumidification post-hurricane, which is really a separate story.
Yes this is what I do with power outage with solar and battery and 5 ton, I have to modify my behavior and conserve, increase ac some from say 73 to 77, shower during the day when there is excess power etc.
If there are clouds lowering solar output the ac isnt running as much either or at night.
If I wanted to run as though the grid was up would probably need double the size solar and battery.