I'm not sure where you are looking on I95 where no RV's are permitted. I've traveled that route south from CT many times by truck.
I'm looking at Google map now and see what looks like an I95 to HI way (9) south in New Jersey will get you there just fine.
I don't live in that area but I do visit it once a year. The traffic will be a night mare if you try this mid day, or afternoon.
I normally enter Jersey City and that camp ground at around two in the morning, and during mid week when I visit there.
I'll not go into exact exits you should take a streets as I hope you're using a GPS to help with the navigation.
I'm sure you already know, Liberty Harbor is just down the street south of the Holland tunnel, a very busy area.
I hope that info helps, and if you would like some feed back on the camp ground, I'll be glad to give my view.
Dan & Loretta, US Army Retired Aero Scout Pilot
2012 Fleetwood Providence 42P Class A/DP
Spartan Chassis, 8.9L Cummins 450HP