I'm not saying i'm right here because I don't know what current NY laws are, having moved in 94. But having had a New York City, carry permit, "i still have an old expired one", are you talking about a New York City, or a New York State. The way a Target permit used to work, was unloaded, in a locked box, to and from the range. My uncles had target permits and hunting licenses, and one was a treasurer of the Glen Cove Pistol and Rifle Club, and I shot there several times, the reason I mention this is a few members had been held up by waiting gang members, who knew they couldn't carry loaded guns when leaving. He had asked me to be watchful upon locking up and heading out, since I had a carry permit. All this was over 20 years ago, so I don't know if the legalities are the same or have changed as far as target licenses go. But knowing NY, I would triple check before carrying with a target permit.
If you get stopped carrying a loaded weapon, with a target permit, you may end up in a bad place. I bring this up only to clarify what confused me upon reading the part about always being on the way to or from the range. If that is the defense for illegally carrying, then it won't fly, and has been tried unsuccessfully before. If not then sorry I misunderstood. The same goes for a premises permit, "if they still have those", it would only good for the place where it was issued. New York takes this stuff very seriously.