Elenor,
I fly quite often with my firearm. I glanced through some of this thread, and saw you were getting some pretty interesting advice.
Keep it simple. Put a good heavy duty padlock on your hard case, inside your regular suitcase. I added a nice bicycle lock through the handle of my case, then wrapped it around the inside "frame" of my suitcase. That effectively prevents any smash and grabs. The deceleration form MUST go INSIDE your suitcase, but OUTSIDE of your hard sided locked gun case. Southwest tapes it to the top of your case, United just sets it in your suitcase, I always ask that it be taped onto my case.
I have only been asked to open my case one time, by the ticket agent. She even touched my handguns to see if the mag was out (she was clueless). After we were done, I asked Southwest corporate if they were allowed to touch or handle firearms, and if the gate agents were certified to handle firearms. They were profusely apologetic, said it would never happen again, that normally the case shouldn't be opened, and that they agents were never supposed to touch a firearm. They assured me that the situation would be addressed, and said that they would make sure all of their employees at that airport were retrained.
I would also put a label on the outside of your gun case (not your suit case) with your phone number, and a statement asking them to call you if they have any issues. When I was flying out of Phoenix one time, they had my bag for 1.5 hours, before they called me to say they wanted to see inside my case. I had to deboard, and miss my flight, so they could look inside (but that is another story). They claimed that it took them that long to find my number...hogwash.
I always tell the ticket agent that, "I am declaring a firearm in this bag."
I have never been asked to demonstrate that my firearm is clear. If that happens, I will ask for them to call airport police to come clear it. With the sheeple today, I do not want to be seen handling a firearm in an airport. I will politely ask for airport police to come clear it, or be there when I clear it.
I don't even lock my suitcase. It looks just like everybody else's bag, and criminals know you usually lock what you don't want them to take. I also double check to make sure my gun case is still in my suit case when I take it off the carousal. That way you catch any problems before you leave.
Don't worry about it too much. Sounds like you have done your homework, and you will be fine.
Cheers,
AG