here's an idea it adds some more miles but I believe the routes are nicer style roads to ride. And that would be to go from Annapolis to Greenbelt/College Park then hop on the Northeast Branch Trail that connects to the Metropolitan Branch Trail and that will take you right to Union Station very close to the National Mall and Capital.

One caveat there is a section between the two trails where you need to go back on the roads so make sure you study that section.