The House is a mess. So is SCOTUS. My proposal for the latter is redefining the Supreme Court as one drawn by lot from appellate judges for each case. This not only solves the appointment lottery. It also incentivises expanding the judiciary, which we need to do, and removes the modern perversion which is the Supreme Court just not bothering with controversial cases.
Most importantly, the edits to SCOTUS can be done by the Congress. The edits to the House can be done by the states. (EDIT: Nah.) Senate requires a Constitutional amendment; that window isn’t open at this time.
The Senate is elected similar to a parliament from other countries. Country-wide votes for parties, with proportional representation. It would balance out the regionality of the House.
The Supreme Court justices serve terms of 12-16 years. Each presidential candidate must select 2 supreme court picks at least 4 weeks before the election, and whoever wins has their picks placed on the court. (After their term, supreme court justices retire to the DC circuit).
This is important to understand, because the 17th Amendment is an on-again-off-again political issue; Republicans have, in recent history, held most state legislatures, so repealing the 17th Amendment would basically guarantee that the Republican Party would control at least one house of Congress for the foreseeable future, and give the party greater control over who is selected to the office.