Now that I think on it a bit....
Something else you could check on, There used to be a group called the Saratoga County council of Fish and Game Clubs. I attended a couple of meetings way back then, when my father was a member of the Snookill Fish & Game club.
This was NOT any kind of offical govt agency, but a meeting board of folks who represented the different fish&game clubs in the county.
If they are still around, getting ahold of them, or any fish&game club, shooting club, or even the boy scouts might be able to put you in touch with someone local who has been through the process and knows the people involved. Guys who still give Hunter safety classes are often well informed.
Get to know some people, and let them get to know you. New York, as you most likely now is NOT a shall issue state. Ultimately, your approval is entirely up to the judge who issues the permit.
You say you have your paperwork ready to hand in? Just curious, mind you, but what does that entail these days? When I got my permit, it included 3 character references (who I believe could not be relatives, and had to be county residents), 4 photographs, and 5 sets of fingerprints, and of course, the investigations.
This was, however, well before the computer age. And here's a tidbit for you,might make you understand how seriously somebody back there takes the permits. I moved out of NY in 79, and around 2002 or so, they sent me a letter, informing me that since I was no longer a NY resident, they wanted their permit back. And they wanted to know where the guns listed on it were.
I don't know what kind of physical permit they issue today, but back when I got mine, it was a green paper embossed with the state seal, with a portion of the embossing passing through one of the passport size (b&w) that you provided. (the rest you never saw again, in some files, somewhere). And the picture was simply stapled to the paper. You couldn't lamintate the permit, if you ever wanted to add any more pistols to it, because the gun's information was typed on the back of the form. Make, caliber, barrel length, & serial number. And the requirement was that, as long as there was space, any additional guns information had to be typed on the permit.
If you haven't already, find out a bit about your local judges. 35 years ago (the past is, however as they say, "a different country....") there was one judge who would only approve a permit for "hunting and sporting purposes". Another one would approve permits for "personal protection" and disapprove everything else.
Trust that if you are anything but squeaky clean in the legal system, it will be found out. But the system, being what it is, anything, no matter how minor or how resolved can influence the decision of the judge. After all, they don't know you personally, now do they? So if you have anything that shows a pattern of what the judge might cosider questionable judgement, be up front about it.
Something as "small" as a series of traffic fines speaks loudly in judge's ears, sometimes. Or at least, that's the way it was.....