Republicans in the Senate would never vote to convict one of their Justices. Even if we retake the Senate (which is not a done deal) we will never get the two thirds majority to boot even one of them. Impeachment is an impossible hill to climb, expansion of the court is not.
I would argue to expand to 15 justices rather than 13. The federal court system is overloaded with cases which slows the whole system down. The solution is to add two new circuit courts. 15 justices, 15 circuits, with one justice overseeing each of them. That would lessen the workload on each circuit. It would also require new territory maps for all of the circuits.
The knock on effect of those new circuit territory maps is that the district maps would have to be redrawn and new districts added as well. That would be a unique opportunity to break up some of the circuits and districts that are dominated by conservative judges, diluting their biases.
To expand the courts would require 2 things. First we need to hold the House, the Senate and the WH, without that trifecta, there will be no expansion. Second, once we have the trifecta, we need to kill the filibuster. Once the filibuster is gone then we could proceed with reforms. Some reforms I suggest:
Expand the supreme court, circuit courts and district courts.
Ban Gerrymandering.
Voting rights protections.
Implement the Wyoming rule. https://en.wikipedia.org/wiki/Wyoming_Rule
Statehood for PR
If you combine all US Pacific Territories, that is enough to make them a state as well.
Consider statehood for DC, so they get full representation.
Once all the desired reforms are complete, bring back the filibuster. But don't bring it back as a Senate rule, pass a law as part of the reforms. Currently, a single senator from the minority can say "I filibuster" and everything stops unless you can muster 60 votes to break the filibuster. The filibuster is meant to protect the minority. Fine. Make the minority get 41 votes to bring a filibuster (meaning breaking it only has 59 votes) and make them vote each day to sustain it. If every senator that wants a filibuster has to go on record to do it, instead of swing state senators hiding behind a single safe senator, it brings more accountability to the process.
By changing the filibuster this way, you still protect the minority right to oppose, but you make them commit to the effort. By implementing it as a law instead of a senate rule, you make the republicans have to go through the full legislative process including presidential signature to undo any of these reforms