Easier solution? Kill the cap on the House seats. Doesn’t require a constitutional amendment, doesn’t make a State out of DC (although I’m still onboard with returning it to Maryland, there is precedent for this as DC used to have part of Virginia), and it evens out representation in both the House and the EC without wrecking the Senate and the EC altogether.
Give the States a number of House seats per 50,000 people (preferably: per citizen), actually make it a range between 30K and 50K to make the number of seats as even as possible and always keep it an odd number. You get a House of 6Kish or so members, but the way I see it, that’s Congress’ problem.
You even out representation between the States so no one State is over or under represented in the House. You increase the cost of lobbying Congress. You effectively solve gerrymandering, it can still exist on the fringes but when medium to large cities can have between 4 and 9 Reps all to themselves it is much less of an issue and unlikely to have much of an impact on the election. You bring the House closer to operating on coalition politics.
Fringe benefits include the necessity for dorms and uniforms and satellite chambers for the House that members can vote from. You can even verify their identities through a combination of simple security measures and biometric sensors, similar to TouchID and FaceID.
Then for every additional House member, you also add one to the Electoral College. It’s not perfectly even because the Senate throws the equity distribution off, but it severely dilutes the EC count that correlates to the Senate.