What have the TSA got to do with it? All they do is screen they don't and can't insist that an airline takes an item on one of its planes !

All those bags that get gate checked have been screened so why should a dress be treated any differently.

You are making a heck of a lot of assumptions - that the flight won't be full, that there will be space in the F/J closets, that the staff will be nice, that 20 other people won't have special items they all want hanging up as well and they ask first.

Stop living in fairy land and make some proper arrangements for transporting the dress that will keep it safe and secure and that don't rely on luck and goodwill.