Holy resurrection. The bigger question is WHY are you being searched or allowing a search?
That is a question but it isn't a bigger one. Why? Who knows. What I do know is that people get their cars searched everyday for questionable or illegal reasons. It takes nothing more than running into the wrong LEO at the wrong time. How it plays out after is, in my opinion, a bigger issue.
Old thread, I know, but a couple comments.
Gas is indeed cheaper in NJ than almost anywhere else in the US. Why? Not sure. All the refineries would make sense, but then you drive just minutes north into NY and CT and prices are some of the most expensive in the country. So I really don't know. And you can't pump your own gas. So that is a strange one.
You have no chance of obtaining a carry permit in NJ. None. They do however have a FPID (firearms purchase ID), for both residents and non-residents. The name itself is a misnomer. It is required to buy ammunition commonly used in handguns, the purchase of long guns, and the unloaded transportation of long guns. They have illegal requirements in order to obtain one (currently multiple multi-year lawsuits over this), and they take illegally long to issue them (also lawsuits involved).
When traveling between states there are two things to consider. State laws, and FOPA. First, the possession at your departure location and arrival location must be legal (state law). If not, nothing will cover your transport. You are breaking the law. Second, do any of the states your are traveling through have strict laws, specifically, more strict than FOPA? If so, follow FOPA. This is almost certainly always the case when traveling through NY and NJ.
Third, something that is even more prominently an issue now, is that believe it or not, while you may be able to transport an un-nuetered AR (for example) through NJ/NY in accordance with FOPA legally, FOPA does not cover magazines, as stupid as that sounds. So if some crazy situation happened in NY, having an AR might not be the issue, but simply having an AR magazine could land you in legal land facing criminal charges. Messed up! Just something to think about.
Quite honestly, I'd be more concerned with NY than NJ these days (when it comes to interstate transportation of firearms.