"Clause 17: To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the Acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings"
There you go. Problem solved. Move "DC" to OK or KS and cede the current area back to Maryland and Virginia. The current citizens of the area known as the District of Columbia get the voting rights they covet and the new seat of government will be moved to an area less needy.