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you don't have any options. as a non-resident you can not be in possession of a firearm.
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That's not completely true but a good rule of thumb if you want to stay safe.
Technically NJ residents can't be in possession of a handgun and the exceptions are just a defense, ie range, on your property, or business, or going hunting. That said if you're transporting through the state and you follow federal rules, ie unloaded and cased, ammo separate, not accessible you can . Never bring hollow points into the state, not even a key chain with one. If you must transport through state I suggest contacting a NJ firearms attorney for clarifications as, you state this state is a nightmare.
Edit: It's also a valid exemption for non residences to attended sanctioned events and go to NJ ranges.