Not a lawyer...and not very computer search savy...sorry
But if there is actually no section of NYS law forbidding loaded firearms in motor vehicles, they have been pulling the wool over our eyes for a very long time. I was taught it was the law in Hunter Safety Classes, back in the 1960s!
It may be worded strangely, it may be in the Hunting regs, it may be tucked away in some unusual place in the Penal code, It may be in the DOT regs, I don't know. But I am certain that it is in there somewhere.
Why not just ask your local police what someone would be charged with (and under) for having a loaded rifle/shotgun in their car, and search from there?
Or, if you have money to throw away, actually hire a lawyer to do the research. Cheaper than getting in trouble with the law, always.
Beat cops are not always well versed in the more esoteric sections of the law, but I would think that for something like posession of a loaded firearm in a motor vehicle, they would have a general idea what section of the law they would be arresting you under. Waste a phone call and ask, the most they can do is give you a wrong answer. And they just might give you what you are looking for.
All else being equal (and it almost never is) bigger bullets tend to work better.