For what it's worth, DCA has had a few random weekday MEP dates available. However, the reservation window opens and closes quickly. (There is a new webpage for checking MEP availability for DLR, different from the old page with the check boxes.)
I've been able to go twice by checking often (most recently June 3, the day before AC opened). I have a feeling those dates won't be available as often in the coming months due to summer crowds and AC crowds. I'm glad they were available at all!
Btw, I used comp tickets at DL/DCA yesterday and it worked out well. Of course, the comp ticket reservations had to be made far in advance.
Good luck!