You have additional worries with NJ law beyond the fed SBR stuff. Grant is top notch to deal with, you should try and deal with him if you really want the product.
I know grant sells the LMTs with phantoms installed, is this what you are buying? (i.e., its not SBR, its 16.1" with flash suppressor installed?) If so, here is what I recommend: Have it shipped to the smith that you want to attach the brake. Keep in mind that not all FFLs can legally receive and posess class III weapons, only those properly licensed. (which most NJ FFLs are NOT) The gun smith can then remove the FS and weld a brake on for you.
Here's the kicker - you need to find a good smith to do it. (BEWARE THE HACKMASTERS OUT THERE WITH NO AR-15 EXPERIENCE!!!)
In the end, unfortunately, it may be easier to just buy a NJ ban compliant upper from somebody else. Though, I really wish Grant could get the business...