Quoted:
Can you be in possession of a box of locked up, secured, stored separately hollow points while traveling through New Jersey to somewhere else?
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Federal safe passage laws (FOPA - 18 USC 926A) does not provide protection from state laws regulating possession of ammunition. So you have to be in compliance with the exemptions spelled out in NJ statutes in order to possess hollow-point ammunition. Meaning - you must be travelling directly to an authorized place for hunting or target shooting, or transporting them from a place of purchase to your residence.
Easier to simply get some non-HP defensive rounds (Federal EFMJ, Hornady Critical Defense, etc.). If you insist on transporting your own HP ammo, find a public range somewhere along your destination, beyond NJ, and plan on going there. Once beyond the border of NJ, you are of course free to change your mind.