For what it's worth, I use somewhat expensive 15,000 mile rated synthetic oil of the recommended high temperatues weight in our built-in generator so as to always be ready for long hot weather runs - just in case we get expectedly or unexpectedly into a situation like the OP describes.
I estimate a fuel usage rate of around 0.4 gallons per hour when powering our air conditioner with the built-in generator, so when starting out with a full 55 gallons in the main engine gas tank we could run our generator for around 70-80 continuous hours before the automatic cutoff that preserves a reserve in the main tank.