So first up does duty to inform even impact the second amendment? I see it as doubtful unless you are referring to some aspect of it that I'm not aware of. But to have standing, you would have to both have been subjected to the law in execution, and also have suffered some kind of harm. But it doesn't appear to keep you from bearing arms or keeping them. It might be considered compelled speech. Now for criminals, it might be considered forced self-incrimination, which might win at court. Once that has one, one could make an equal protection claim.
One gun a month has tons of people with standing, but just isn't the best case out there, especially if you have cases pending challenging permitting as a whole, which could potentially take this with it. This is likely just sitting on the plan B shelf waiting its turn.
FID - permitting is being challenged. Just challenging it in NJ isn't going to bring much to the table at this point and time. IT may come if it is needed to generate a circuit split or after SCOTUS sets precedent.