Uber. You aren't on airport, so no need to use an Dulles Taxi if you do decide to use a taxi (stick with Red Top).

There is absolutely no tolerance for being late for those tours, so better to be 30 minutes early than 1 minute late. Leave at 8:30 AM and wander across to the tour staging area.

Call the Willard the day of. Bet something opens up and you will just arrive more tired at 2:15 AM, but at least sleep in a bit later in the AM.