I will be going for a short trip to DC in November. And where I live, there is no Adventurer's league running. Would love to play it, but I know Encounters usually run on Wednesdays, that's when I am on my plane back 
Is there any chance to play somewhere, and if it is just the home version of ther Starter Set adventure?
It doesn't perfectly suit your request, but I'm running an every other week session of 'Lost Mine of Phandelver' on Sundays in Culpeper, VA.
[note: Culpeper is a solid 90-min drive from DC... and I realize it isn't on the days you're interested in ]
The Nov 16th session would be in the early afternoon, usually 1230-330. By then, we'll be about 8 sessions into the campaign and the other PCs will be 2nd to 3rd level.
We usually play with a team of five, so we have room for a guest player.
If you are interested, reply on this thread and then we can take it offline to private e-mails.
-Dean