They called back with a quote for replacing the engine. Engine $1,296, shipping, labor and misc parts $644 for a total of $1,940.
The A/C is on a 40A breaker, so 40x240 = 9600W.
The well pump is on a 20A breaker, so 20x240 = 4800W.
I think the 15KW unit should be able to start the AC as long as the well pump doesn't happen to be running at the same time. The ovens are not on the generator panel, nor is the water heater or other electronics except for the fridge/freezer.
I'm waiting to hear back from them to see if they will put it in writing that this 15kw unit will reliably be able to start the AC and I also want it in writing that the new engine comes with a 3 year warranty.
$2000 to swap the engine seems a bit steep when a brand new 17kw unit with the digital nexus controller can be had for $3,390...