I was told by someone at my local NYC range NOT to contact 1PP as it will only make them angry. The frame of the gun is what has the serial #, so that's what's registered on your license. There are so many barrel conversion possibilities--.357 sig/9mm/40, .45/22, etc.--it would seem crazy to get your license amended to reflect every possibility since they don't specifically tell you to, UNLESS the issue is you buying or transporting ammo for a caliber that's not otherwise listed on your license.
If you do contact 1PP, please let us know how it turns out.