or you could do the following:

1) Your suite must have come with a cover -- a black plastic zip up.

Take that onto the plane and at the door to the plane, ask the FA to hang it in the galley closet. or you can hold in in your lap and once the overhead space is full, just put your above everyone else's and be the first to take it out.

I fwle ELP-LAS and did not check it in. Also, do not need to iron.