-We can become a state two ways as provided by the Constitution.
-The District has for long periods of time on and off (currently off) lawfully had voting representation in the House.
-We had a Constitutional Convention already and submitted a proposed Constitution for the State of New Columbia which failed to get the necessary state ratification.
-There is nothing to prevent Congress from creating federal enclaves (all federal buildings) exempt from District law not unlike the hundred plus foreign governments on foreign soil here.
-There is nothing to prevent the Federal Government from exempting District residents from Federal taxes not unlike citizens in US territories.
Shrink DC to only contain the Capitol, the White House and many of the Federal buildings surrounding them. Now you still have your federal district, and the residents can either form a new state or join MD or VA.