So, I'm certain OP already knows this, but for those who dont:
Airport operations AND airport security coordinator here (Edit: Some folks have asked what this is. I am responsible for implementing/executing commercial airport security programs and certification programs):
Airlines are not liable
for lost/stolen/damaged gear. My suggestion to anyone traveling with firearms is to take photographs, especially with personnel if able. Also, take a note pad and note the names and badge numbers of anyone involved. Make sure to request the TSA's "SIDA" badge. In this way you can hold individuals responsible pursuant to 49 CFR Part 1542 and 14 CFR Part 139 if any of your gear is "lost" (read: stolen). 1542 is airport security and 139 is airport certification, which contains elements of security standards. A bag of guns disappearing is cause for audits from the FAA under both of these regulations.
I once flew with a similar setup, but in a locking bag instead of a case like that. The airline lost about 9 firearms, two cans, ammo in a separate bag, etc etc. When I mentioned it I got the standard "Sucks to be you, nerd. File a complaint online and well get back to you" response.
My bag was found (no joke) in 7 minutes when I had my friend that is a local news camerman show up with his crew to report AA losing not just a firearm, but two bags
full
of guns and ammo. Having the names, times and badge numbers of the people involved would have made things significantly easier by forcing accountability.
TLDR; If you give a ramp-rat a chance to steal your guns he will. They average $12/hr. Take photos, names, and badge numbers when checking in firearms. Don't just assume they will arrive at your destination.