Never had problems with my 13 cu ft on a carry on in Mexico, nor in Ft. Lauderdale. Had problem only once in Detroit metro. The TSA supervisor refused to let me through until he checked his rule books. His employees knew the rules and he didn't. They had to put a penny inside and turn the xray to "deep fried" to make sure no contrabands are inside. As I understand, some airliner charge you xtra money to check in tanks. Fortunately, most airline has websites that will tell you if they will or will not charge for scuba tanks. Spirit airline does not, so I now carry my tank in check in luggages if flying with spirit.
I would remove the valve and pack it padded separately from the tank. I would wrap a garbage bag around the tank to keep dust and moisture out, and make it easy for TSA to remove and observe or test the tank. I can guarantee you will get a tag inside your bag with the tank - saying that TSA has sniffed all your dirty underwear that was packed with the tank.
Oh, for your information, I got through custom in mexico REALLY fast when I packed my dirty clothes together with my dive gears!! One look, and the girl waved me through.