#2 and #3 Nail it.
Even if they do ask for you to open the case, they don't inspect it.
I've flown out of DIA 10-15 times now
Pistol: Sign form and tape it to outside.
Rifle: open case, throw in signed form. Lock back up.
That explains it. I've only ever flown with pistols, never with long guns.
"We've done the impossible, and that makes us mighty."
Nathan Fillion, "Firefly"