No way would I backtrack that far out of WAS. You're looking at 3+ hours of flight time to DFW from IAD and then 2.25 hours of additional flight time from DFW.

Do the DCA-JFK (with the 3 hour layover), have a nice dinner at the Chelsea / Soho lounge (depending on your FF status level), and sleep on the plane. Be sure to book the late JFK-LHR flight (9:00 pm or 10:00 pm).

Not to mention the fact that your connection time in LHR is really really tight.