Your understanding of the AR modifications seems spot on – pinning the stock and replacing the flash hider with a pinned/welded muzzle brake should keep you in the clear. For the "Other/Non-NFA firearms," ensuring the barrel is at least 12.5" and adding a vertical foregrip should comply with NJ regulations.
As for moving back, I feel you – I recently moved to a new state, and it was pretty challenging. A friend recommended a moving company that really helped simplify things. If you need assistance, check out https://threemovers.com/what-is-considered-long-distance-for-a-moving-company/ .