My two cents, but I am nobody special.
Any NJ Dealer (01 or 07) can accept NJ "Assault Weapons" as stated above. They are exempt for possessing for distribution to LEAs, Military, and LEOs with a letter. Per ATF Rule 2010-10, the compliance work MUST BE DONE by a manufacturer, because the firearm is being modified.
To quote ATF, "a dealer-gunsmith may make or acquire his/her own firearms, and repair, modify, embellish, refurbish, or install parts in or on those firearms. If the dealer-gunsmith then sells or distributes those firearms for livelihood and profit, the dealer-gunsmith is engaged in his/her own business of manufacturing firearms."
Technically, the firearms would be logged into the NJ SAW Book, modified, logged out and into the regular book for resale to Joe Blow Citizen, BUT ONLY BY a manufacturer, per the ATF. And of course, new manufacturing markings need to be applied.
But in reality, here's how it works. Or rather, how it is "officially" done. The savvy NJ FFL01 takes possession of the evil weapon, does the modifications to make it NJ compliant, then logs it into his regular book, as it is no longer a NJ "Assault Weapon". Federal Law 478.125(e) allows firearms to be logged in by the end of the next day. So technically, the firearm is in limbo during the modification period.
In an Interstate Transfer, as is being discussed here, one may bring up the argument that the customer is the owner, and that the FFL01 is acting as a gunsmith, and is legally able to modify the firearm per the ATF Ruling. But where does ownership begin? Payment, approved NICS, or a completed 4473. This is a gray area IMO.
Sometimes it is best to let sleeping dogs lie.