I wonder if you could enter "All lawful use/carry" as a reason?

Seriously, that's a messed up system. The only time I've ever had a firearms permit or license that required anything other than personal info like name and address, was when I was active duty; my concealed carry permit mentioned the gun(s) I had qualified with and allowed to carry on the plane. It didn't mention SNs just type, like M56 or M9.