Seems like each station has their own way of handling things. Hilo and Las Vegas you need to open the gun case so agent can inspect it. Ammo in same case ok. Honolulu is the same except agents I had don't ask to inspect firearm. Phoenix, ammo has to be packed in separate suitcase, which means you will need to check in and pay for two bags. I have Pualani Gold, so I get two bags free. After agent inspects the gun and ammo, they take you directly to TSA upstairs where they open and inspect the bag in front of you. You then lock it up and leave it there. I thought Phoenix would be the easiest, but it was the most humbug of all.
BTW, HA recently raised their check in bag fee to $30 for the first and $40 for the second to the mainland. So if you don't have a Pualani Elite or Premier Club membership, it might cost you as much as $140 to take your gun to the mainland round trip.