I do not know anything about GNP, I always thought it was for groups not individuals but that could have changed , therefore I stopped looking into it . I do not think they have electric sites and only 20 or so sites. Did you call there already ?
Maybe this will work, maybe not, either way, here are the links. 2 CG's listed here with phone numbers .
https://www.nassaucountyny.gov/2812/Nickerson-Beach-Parkhttp://www.nassaucountyny.gov/2802/Nickerson-Beach-Park There are many links about the area boardwalk here . Train service. you check rates and times etc .
http://www.longbeachny.gov/index.asp?Type=B_BASIC&SEC={4211D402-CE99-454B-B0E2-8B431D6087C5} If you decide to do this , do it ASAP , the CG's fill up real fast.
PM me if you need more info.
Bob