The problem is LEOs are political, they have their sides, they also follow orders from supervisors on up. An officer can pretty much arrest anyone for very little and "just allow the courts to figure out the law". You couldn't pay me to enter NJ with a firearm for any reason (event, range visit, through-travel, etc), let alone with HPs under any circumstances. An officer there who wants to, most certainly can, and will, make the arrest, turning your life upside down while they go home satisfied at the end of their shift.
The LAW is NOT on your side. Innocent until proven guilty is pure BS today and "The LAW" will differ from one judge or jury to the next depending on how its twisted. Yes, its sad.. very very sad but that's the truth.
Best thing.. don't provide them with ammo against you (pun intended). While they might be legal, explain that to your wife and kids sitting at the dinner table here in DE while you sit waiting for your lawyer in a NJ jail cell.