No help with the technical aspect of the OP's problem but can say that every state park I've ever camped at in the NE gives specific hours for running a generator. As long as that is adhered to he should be fine.
Now from a different perspective have you checked the weather forecast for the time you are going? You'll prolly be more in need of a heater over the A/C despite it being unseasonably warm and humid currently (GRR!). With no generator you won't be able to use microwave, wattage hog, that it is but you will be in the great outdoors;).
