I went through the process for the NY permit when I was there. The restrictions are between you and the issuing Judge. From a law enforcement point of view you have a permit. They are not concerned with the restrictions and violating them carries no criminal or civil penalties but the Judge can revoke your permit if word gets back to him that you were stopped and obviously not on your way to or from the range or the woods. Most Judges consider all outdoor activities: hiking, backpacking, etc. to be included in the hunting restriction. You cannot just say you are part of a 24/7 club, you need to go join one. There are several in the area, gun-ho-a, in Schenectady is a good one but I believe there is a multi-year waiting list for membership. Once you join one put a range bag in the car with targets, eye and ear protection, and some ammo and leave it there. Then you are always on your way to the range. Not from the range since that's easy to confirm. I had my permit in Fulton county which was also very CCW friendly. The standard was that after you had your permit for one year you went back to see the Judge and asked to have the restrictions removed. Anyone I know who did this had them lifted. After a year you have proven yourself responsible.
Good luck and congrats on making it through the muddled NY process. Since I left NY I have obtained my Utah non-resident permit and my KS resident permit and the effort for both combined was 1/2 what it was to get it in NY. Of course here in KS you don't need a permit to own a handgun, just to carry concealed. If you want one for hunting, hiking, target practice, etc. you just go to the store and buy it.
In reading through the NY penal code covering handgun permits no place does it say that you have to tell an officer that you are a permit holder or that you are carrying. Some states require to you to tell the police when you are stopped e.g. for speeding, that you have a handgun. Since you are not required to disclose it you shouldn't if you are carrying and have restrictions on your permit.
http://public.leginfo.state.ny.us/me...MMONQUERY=LAWS See penal law section 400