I like what you've suggested, Swerd.
It strikes me that the beginning of this would need to begin with a concerted coordinated effort to clean up congressional districts boundaries (including the breakup of all gerrymandered districts) to meet the basic guidelines and spirit of the goal therein. The Supreme Court seems to largely be of the mindset that this falls to the states... and their gerrymander-protected legislatures... to rectify.
If I understand the history of this issue correctly, the US Supreme Court has kept it's hands off of issues of state politics. Deciding the locations of districts, both for US Congress and for state government districts, is given to the states and not the federal government. The same is true for the process of running elections.
Several states, to my knowledge, have recently tackled the gerrymandering problem, Pennsylvania and Virginia. In Pennsylvania, the state supreme court ruled that gerrymandered districts must be reapportioned. The GOP controlled legislature refused to do that, and the courts themselves stepped in to reapportion districts. I'm not sure what has happened more recently.
Similar things happened in Virginia. In that state, recent elections have resulted not only in Democratic governors, but in 2018, a Democratic controlled state legislature was elected for the first time since the 1980s or 1990s. They are in the process of creating an Independent Reapportionment Commission, that will replace the politicians in the state house. I hope similar things are occurring in other states. Texas and Wisconsin come to mind, but there are others.