One other thought I just had was that you could consider taking grabbing a bagel or muffin in the airport and take a taxi from airport and have them drop you off close to Lincoln Memorial. This is the furthest spot away from restaurants, museums and metro. You could do the Lincoln, Vietnam & WWII memorials (outdoor, accessible 24 hours) first thing before the museums open up and eat your breakfast snack outside.

You could then make your way down to the museums, Archives, find a place to eat lunch and then eventually take the Yellow line back to the airport (or just hop a cab) at the end of the day.

I do not like DC taxis and usually try to avoid them, but in the morning it might be something to think about to allow you to just walk the Mall in one direction rather than having to do an "out and back".

You will hit a little rush hour traffic in the AM assuming this is a weekday trip, but it should be manageable.