A point to keep in mind...
If the "24 hour club" you join is 5 miles west of your home, and you get stopped 5 miles east of your home, it is a real stretch to state you arwe on your way there.
Also note that different counties have different rules regarding how hunting/target restrictions are regulated and enforced. The very tight Suffolk county restriction is a great example. If you get stopped outside of your own county, you are likely to be judged by that county's own code/restrictions. Especially if you are nowhere near that 24 hour range.
Yes, I fully understand that the violation is administrative. However, the county still has the power to revoke. Once they do, I think it very unlikely that you will get a new license for a while, if at all. Without a license, then you have to get rid of all your handguns. Any carry at all without that license is then a felony. For me, too much of a risk. YMMV.