I know there was a thread on this topic a while back, but remarkably, fares have actually
dropped a bit since then! And yes, the LAX-JFK-LAX legs are on the A321s with lie-flat seats.
(Even JFK-MIA-JFK are on a 76x & 77x with lie-flats!)
Dates appear to be quite varied, but here's one such routing:
https://goo.gl/fZLu2s
It requires an overnighter in PTY -- plus, obviously, a red-eye on the LAX-JFK leg -- but the return trip can be done in a single day. It's also slightly lower if you stay in PTY for 2-3 days. Further still, AA extended its bonus-miles promotion into 2016 (though alas, not the one with 3x EQMs).
Edit: I miscalculated the bonus-mile count for EXPs (I mistakenly based it on the bonuses for full-fare tix), but general info on the promo is here: http://www.aa.com/i18n/urls/aadvanta...itle=moremiles
Edit #2 (1/26/16): I can't change the thread title, but rates are now available on a similar routing -- including lie-flats on the transcon segments -- for as low as $437!!!