I edited my post while you were replying, to note that JL does offer the 787 Sky Suite out of DFW four days a week (Mon, Wed, Fri, and Sun), and also to suggest routing JL via other US cities (JFK, ORD, SFO, or LAX; JFK has the advantage of a longer flight, so more time to sleep and relax). If you're buying a DONE3 product, you can add extra domestic segment essentially for free.

I'd opt for JL's new Sky Suite product over AA's J, personally.