I don't think a surge protector will work when plugged into a generator. My old surge protector would not, but I cannot say for sure if all are like that.
I run our air with a Champion 3100. We have two units, a 13K and a 15K - we usually run the 13K but I've run the 15K on the generator before. You have to be careful what else you run and remember that the fridge will switch from gas to electric once the generator fires up unless you lock it on gas mode. That and the microwave will trip the overload

I noticed you're in Durham - if you're not too far from me I can let you try to run your AC on our Champion 3100 if it helps you figure things out. It's light enough I can toss it in the back of the truck pretty easily. Just message me if you're interested.