I flew a few years ago from Las Vegas to PHL... I laughed as I got on the plane because no one had a clue behind the southwest counter.
I approached the counter, told the ticketing agent what I had, what I was doing, etc... had two pad locks ready to put on the case, etc. An Air Marshal friend of mine had told me what the procedure was and it sounded easy enough.
The lady behind the counter was like Ok.. here.. fill this out. they put a tag on the already locked case and gave me one too. I asked her if it needed to be verified that it was empty, locked properly, etc... nope. She didn't want to see it. Hmm. ok. So after I lock this case how are you going to inspect it? She looked at me with the deer in a the headlights look. Okie Dokie!! I'm getting on the plane, lady.
I had a TSA lock on the bag the gun was in along with a zip tie. It was never opened. I'm sure they could xray the bag, but they never opened it.
It was very easy to transport a firearm on SW.
Moosie