And the proposed battery solution only works at up to 3kW. My electric range uses more than that, and my water heater, clothes dryer, and aircon each come close.

And, sure: I can get by very well with refrigeration, networking, computing and/or TV, and lights during a power outage. But those loads need to be segregated, or it just doesn't work. That adds more expense.

And since those segregated loads don't even come anywhere near 3kW, it isn't clear to me how I'm to be maximizing my local use of surplus power events.

There are grid-interactive battery solutions from companies like EG4 that can go betwixt the entire house and its grid connection, but this isn't it.

Why do you need to segregate them? Can't you switch the rest off? Or is the problem that otherwise you'd supply neighbors as well?