I would do Uber and leave at 8:30. I agree with Often1 that if you can get into the Willard, even at 2 AM you are going to better off. They are doing a lot of emergency track work on Metro, and it is making traffic a nightmare for folks in the area as they adjust to finding alternate ways into DC.

When the emergency track work started a few weeks ago, there were reports of the rush hour traffic extending the rush to 11:00. Here is the link so you can see the schedule. http://www.wmata.com/rail/trackwork.cfm

Best of Luck.