The only thing you can do is cooperate. I have a lot of Jersey friends who shoot, and as far as I can tell in very few cases are the police purposely "suppressing" your application. Most of the time it really does take them a long time to get through, and it's the law's fault, not their personal fault. If they're giving you flak about "why would you need a gun?" then it's a different story. Thankfully I have not run into this during my time here, and the police I have interacted with have conducted themselves professionally.
One guy's permit, that I know of, took seven months because of the backlog of permit applications post-9/11, when everyone wanted to get a handgun. Mine took two months, and I know for a fact they did it as fast as they could (it was my SBI check that took awhile). If your references haven't responded to the police queries, that could also be an issue.
Subsequent handgun permits should take less time because there is less involved with getting those. Likewise with an address change, my local department was extremely professional and helpful in that regard.
In short, you have no choice but to be professional yourself, and hope that this generates a professional response.