Don't even bring a firearm with you when you visit the notorious Garden State; and you can forget about federal, 'peaceful transportation' laws. NJ state firearm laws are, at best, arbitrary; and you may expect them to be enforced that way, too.
A few years ago a number of PA pistol shooters refused to attend a championship pistol match being held in New Jersey. Why? Well, among other things, by a strict interpretation of NJ gun laws these contestants couldn't even legally purchase ammunition in New Jersey; and staying overnight in NJ while in possession of a firearm(s) is legally tenuous. In fact just stopping at a restaurant to eat, or even to pump gas, while attending a NJ pistol competition opened up out-of-state pistol competitors to NJ state prosecution.
By the letter of NJ gun law, simply possessing a firearm, there, without a NJ Firearms Owners' ID card is illegal; and it's, 'no matter' whether or not you live in New Jersey. If you haven't got an NJ state ID card then you're in (technical) violation of NJ state law.
I've received several invitations to travel into NJ in order to attend this or that match or gun range; but, on reflection, I've always decided not to go. I know, at least, two out-of-state gun owners who were, 'crucified' after being caught with a firearm by the New Jersey State Police.
Although often denied I know, for a fact, that a state police driver's license check (wants and warrants) will bring up information that an out-of-state driver is LTCF in his home state. Once that happens you're going to be treated and questioned in an entirely different manner by the detaining trooper.
I'm not saying either of these gun owners didn't run afoul of NJ firearms laws; I am saying that each of them - who were, otherwise, law abiding and legal gun owners - were, 'crucified' for relatively minor gun infractions of New Jersey state law.
One PA gun owner, whose tale of woe I will never forget, had to submit to a scrupulous NJ state police search of his vehicle - Which included stripping his infant son in order to look inside the diaper! This fellow got a suspended sentence from the NJ court as well as an opportunity to have his newly acquired record expunged after 5 years; BUT he, also, ended up with a whopping $25,000 dollar legal bill!
What did this fellow do? He said that he was late for Thanksgiving dinner at his parents' house, went racing down I-80, got stopped by the NJSP, and suddenly remembered that his, 'car gun' was inside the vehicle along with his wife and baby. While the State Police were, 'running his license' he was asked, 'Do you have a firearm inside the vehicle?' When he answered honestly - Curtains!
Federal Gun Law for CDL Drivers | AskTheTrucker