If you want to find Americans at their most american, DC is probably a good place to go, haha. Not surprised that your Englishness feels extra out of place there.
It seems like a lovely, colorful city... sadly I have only gotten to spend about 6 hours there while on tour, trying to play a show that ended up cancelled. OOPS.
I really got a feel for the downtown area much better this time. It's very walkable. There are plenty of reminders of Independence and the Constitution. Being there on Sunday is great because you get to see all the families learning about their history.