Inspired by the state named roadways in Washington DC, a solution to the DC representation problem presents itself. Rather than DC being a state of itself (it is smallish, certainly in size, but also in population), which clearly raises the ire of Republicans who would be loathe to create 2 Democratic Senate seats, or being functionally retroceded to Maryland (which gets Maryland one more representative, but diminishes each Marylander's vote for Senate and creates new demands on taxpayers), we could divide the District into 50 districts, and assign each to one of the fifty states. The districts should be approximately equal in size (~12000) people and area (~1.2 square miles).
The elegance of this is that everyone in Washington would get a federal vote, some people in Minnesota, some in Florida, and so on. Every Senator and 50 representatives would all have some interest in the District of Columbia, as a good number of their constituents live there. Washington would no longer be "there", but instead be part of all of the United States. Incumbents in Congress should vote for it, since they have an advantage in campaigning in this not inconsequential district of the District compared to rivals.
We could tie each district to the state avenues, so, for instance, Minnesota would get a chunk of DC that is along Minnesota Avenue, say around the Minnesota Avenue Metro Station. Florida's chunk would be in part coterminous with Florida Avenue, and so on. We could further encourage Senators and the Representative to stay in the part of DC that is in their Congressional district. This would disperse at least 50 Representatives and 100 Senators who have a nasty habit of co-habitating to no good end, and this would further their feel for the city.
The link below illustrates the concept for Minnesota Avenue.
View Minnesota section of DC regional scale