> Ditching first past the poles and mitigating gerrymandering would also obviously help.
Mitigating gerrymandering is a lost cause with first past the post because someone has to draw the lines and whoever is in the majority at the time is going to find a way to benefit themselves. It's especially hard because in a state which is e.g. 60% for one party, drawing the lines in a "normal" way can pretty easily result in a bunch of districts that are each 60% for that party (i.e. they get 100% of the seats with 60% of the votes), and getting it to not do that is the thing that could require a bunch of strange looking lines.
Whereas if you switch from first past the post to score voting, gerrymandering is basically irrelevant.
First past the post de facto disenfranchises the majority of the district including members of both parties whenever the split isn't almost exactly 50:50, because then the outcome is effectively a certainty even if significant numbers of voters change their minds. Everyone who supports the losing major party or any third party fails to benefit them, and everyone who supports the victorious major party in excess of what they needed to secure the district is also not moving the needle even a hair.
Whereas with score voting, you can have more than two viable candidates, and then hyper-partisans can't win in a district where 40% of the voters hate them because they'd lose to a member of their own party, or a now-viable third party candidate, who can appeal to voters on both sides. Changing the composition of the district changes which candidate wins even when the change doesn't put a different party in the majority, and with more than two viable parties there may not even be a "majority" party anymore.
The problem is someone got the Democrats to start promoting IRV, which is barely better than first past the post in many cases and actually worse (i.e. more partisan) in some pretty common ones. Which in turn got a lot of Republicans to start opposing all voting system reforms because they didn't like the results. Meanwhile they would both benefit from using score voting instead of FPTP or IRV. I mean seriously, does either party actually like this partisan hellscape?