>Doing the math, I'd need something approaching 800kWh of storage to ride through this kind of event (7+ days)

How airtight is your House? You may be better off with a tighter house to reduce the infiltration load from the outdoor air and possibly section out the house so that post hurricane the primary living spaces are the only spaces that are constantly getting fresh air and there fore humidity load and for the non primary spaces, you dehumidify once and hold it there.

>I think a simple generator on an ATS remains undefeated from an engineering perspective. If you have an air cooled unit

Yes, if your outages are under lets say 10 days a year a generator + fuel will be orders of magnitude cheaper wrt TCO, unless your grid is super expensive.