“but anyone caught with a gun without the appropriate license stamp goes to jail for a long time;”
Ok so are you going to require a drivers license and special stamp for all the other Constitutionally protected rights?
Owning a gun is not a constitutional right for everyone. Here in Colorado, you cannot buy a gun if you are under the age of 18, and people who have been convicted of domestic violence cannot own a firearm. As far as I know, those prohibitions have never been challenged in court on constituional grounds.