Until $$/watt storage comes down significantly, my interest in whole-home battery backup systems is in theory only.
In terms of space (by total volume, not just square footage) wouldn't it be better to have fuel storage and a small generator rather than using the same space for batteries? Plus, the cost. A battery-based whole home backup power system with enough reserve to handle a 3-5 kW constant load for more than a score of minutes is going to easily run five figures. From what I'm seeing you will be $20,000-ish into an installation for that kind of capacity.
Briggs makes a 10kW standby generator that I see priced at around $2700. Runs on propane and has a rated consumption of 1.2 GPH at 50% load, so figure 1.5/hr just to be conservative. New 250 gallon propane tanks are approximately $1500. At roughly $2.50 per gallon that's $625 for a fill. Add in another $1000 for wiring and incidentals and you're $6000 into a system that is ready to provide 150+ hrs of 24/7 power as-is, or several weeks if used ultra-conservatively and supplemented with a good heating stove and a couple of inexpensive consumer-grade 100-300 watt solar panels for low-draw loads like phone chargers and such. The remaining $14,000 (vs. the battery system) is money to spend on food, ammo, and more fuel. The system can also be refueled indefinitely, and at any time of day, vs. the battery system's inherent daytime and meteorological condition restrictions.
Brad