There are two things I've done. Others may have a better answer. The second on the list below is the most practical and what I recommend. The first is something I've been playing around with:
1. Lock the whole dang case:
If the hard sided luggage Latches closed, as mine does, then you just add a hasp and padlock it. You don't put the gun it's own case, you make the WHOLE SUITCASE the gun case, so you can use your own lock and TSA cannot have a key.
Think of it like if you go hunting and have a nice rifle case, and you put a change of clothes in it.
At first I thought I'd get the book thrown at me trying this. But I followed it to the letter of the law and haven't had any issues so far other than some damage to one of the cases where it looked like they tried to pry it open. But a little Flitz on the spot and it came right out.
2. Mount a loop or hasp into the inside side panel of the hard sided luggage:
If it's thin, the screws will poke out a bit. I just filled a little cap with locktite and put it on the outside, over the screw. Blends in with all the other bumpers and zippers and etc.
It's by far the easiest way to do it, and was a 10 minute and $10 sort of fix, but well worth it.
However, it's not as fun as experimenting with option number one above.