This should help you a bit. NY is tough. I relied on the federal statutes and obeyed all traffic laws. Guns and ammo were locked up in separate cases in an "obscure" part of the vehicle. I also had a lot of info "on-board" regarding the competitions I was going to attend (which were all outside of NY, but in the direction I was traveling". I've also linked the NY travel rules. Very strict.
NRA-ILA :: Federal Gun Laws
NRA-ILA :: Gun Laws
Just "Click on NY and you get a concise summary.