Already titled, it's easy as crossing your T's and dotting your I's, regardless of how the title reads.
Not yet titled and still on MSO, again, it's as simple as calling (609-292-6500 extension number 5064) the special titles division, and asking for the "kit car" package. Follow what is in the package to the letter, and besides the coin flip as to which inspector does the initial "safety inspection" (I liked Morristown for this as they were kit car friendly, but after Hurricane Sandy, it was permanently shut down after getting 11 feet of water flowing through it). Asbury Park is hit and miss, there is one inspector that hates his job, and thus makes your life as miserable as his. Have not had anybody complain about Westfield or Winslow, but that does not mean one is easier than the other, as it all falls to how good or bad a day each inspector is having.
Where people run in to problems is not having the paperwork in order, or tries to reinvent the wheel (so to speak) by trying to title the car as a "historic vehicle" with a 50's, 60's, or 70's year filled out in the paperwork. The Special Titles Division is not full of stupid people, and they will reject your falsified paperwork and maybe even subject you to a NJ State Trooper hands on inspection, in search of stolen parts for your attempted deception.
Bottom line, get through the safety inspection first by following the letter of the law and everything as spelled out in the "kit car package"
Hope you find this helpful as well.
Bill S