Couple of points here:
1. The serial numbered part of the firearm (the lower of an AR-15) is what is entered in the NFA registry.
2. Barrels do not matter. One may purchase and possess short barrels or cut them short w/o breaking any laws, EXCEPT, if you possess the parts to make a complete SBR.
3. As stated, only full-auto is permitted in NJ. No SBR, SBS, Silencers or DD. Even though there is no law description of an AOW, it is advisable to not own one.
4. A legally registered NFA item, other than an AOW or FA, will not be transferred to a NJ address. (there are ways for a resident to own them)
5. There is no manufacturing of a firearm allowed in NJ unless one has a manufacturer's license.