Some thoughts. None is particularly appetizing or comforting, but what the heck.

-- have you been watching the DCA-JFK flights to see if they typically land early?

-- have you considered DCA-LGA/JFK-SFO? (I know, Van Wyck traffic during rush hour is not idea. Just raising it).

-- Can you do WAS-NYC the night before to avoid the early am flight?

If nothing else, these other options should make the 6am flight more appealing!