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If I understand it right, if I have my solar inverter in off-grid mode and it decides it needs generator power (i.e. because my batteries’ strength of charge SOC reaches a set point like 20%), then when my inverter fires up the generator it tells the generator to run at full capacity until my battery SOC is up to a set level (i.e. 30%) and tells it to shut off. So if I have 60 kWh of storage, 10% of that is 6 kWh. That's about 40 minutes of run from a 10kW generator.

You should do a little more research on how this all works together. Unfortunately people who sell generators often try to upsell larger capacity units because they charge so much more for them. It is often said that for an off the grid system that you should buy a generator that is twice as large as the inverter in your solar system. The reasoning behind this is murky at best. In reality your generator should be just large enough to handle the maximum load that you will be putting on it plus a little fudge factor to handle equipment with large starting loads.

Here are a few figures from our past experience to think about.

Even on natural gas that still costs us just over $1 per therm, the generator still costs around three times what the power company charges for electricity... currently $.10 per kwh. Because our generator runs more efficiently on natural gas than gasoline 1 therm for us is the equivalent of a gallon of gasoline. Gasoline is now up to approximately $4 a gallon here in Washington. So you can see that electricity generated by our generator using gasoline would cost us around $1.20 per kwh to generate. This is based on our usage patterns with a 5kw generator and an average 2500 watt load.

Good point on the price of nat gas being lower than gasoline.

But if I convert my two natural gas appliances to electric, I'm getting rid of my natural gas bill. Along with it goes the $11 or so monthly fee I pay just to stay connected, not even counting how much I pay above that for per cubic foot usage. So that's part of the math.

But this is only if my power company forces me to pay the "solar fee" of about $54 per month on top of the $15.86 per month we have to pay just to stay connected to the power company (before paying more per kWh usage). If I never have to pay that, then I'm happy not buying generators anyway. The power company is my "backup" whenever my batter backup isn't enough. But if I have to pay that fee and cut off my connection to the power grid, I'll gladly buy about 1 or 1.5 gallons of gas per month to feed a 10kW generator (maybe a 2nd 10kW generator as a backup to that or if I have company over while it's raining) over having to pay $11/month to the natural gas company on top of the cubic foot usage when I rarely use my generator -- after buying a really expensive natural gas generator.

Keep in mind that if my inverter was to kick in the generator when my SOC gets to 30%, I still have 10% my inverter pulls from the batteries (before it has a 20% SOC cutoff to not pull from the batteries at all), which is currently 3 kWh (it'll be 6 kWh if I double it to go off-grid). So that's 6 kWh my inverter can pull the batteries from while it's getting 10 kW from a generator, before it gets another 10 kW from the other generator if it needs it.