I use to live in VA so I never stayed on the bust to Le'enfant so I wasn't even thinking about that, but it is solid advice.

I can't remember which office you need to contact, but there is a way to get a tour as a int'l visitor and sit in the senate or house gallery, a gallery visit is interesting for about 2 minutes unless someone is making an important speech. Unlike the House of commons, there is no class separating the visitors gallery from the floor. Call the Capitol switchboard at +1-202-224-3121 and ask about int'l visits and someone will help you. The line is staffed 24/7, but if they have to transfer you the office you get transferred to wont be.

You mentioned you would like to get pictures in front of the monument, if you are serious about this, you'll need to get a taxi to take you because you won't have enough time to take public transit to them and visit the other sights.