With the judicial branch I honestly have must less to suggest. The Court is an appellate tribunal; even with those few matters falling within its original jurisdiction, such as suits between states, it really acts as an appellate court reviewing the conclusions of a Special Master.
I would retain the present method of appointing justices, though I would hope that the Senate as reconstituted would perhaps more aggressively exercise its prerogative of advice and consent.
The great issue with the justices is keeping the judicial function to the judicial function. Constitutional and statutory review necessarily implicate policy choices. All justices, in one way or another, eschew the notion that they are engaged as a sort of super-legislator. But all, at one time or another, give in to the temptation--even if we can't always agree when they have.I know of no way to solve that problem (not, I would hasten to add, a problem on the scale of money-talking that got me started, but, while I'm solving the nation's problem, why not?). But one approach is to give the justices a legislative future, i.e. limit their terms to, say, ten years, and then have them rotate into the Senate, like other magistrates.
This would not of course guarantee that they wouldn't stray into the legislative function. But it might give them a sharper sense of the distinction, in a personal way. And they would have a distinctive experience to bring to the Senate, both in crafting legislation with judicial review in mind, and in passing on presidential nominees.
One other point, perhaps not so minor. I would have at least a third of the Court positions filled by non-lawyers.I know, we typically no longer allow non-lawyers to preside over even municipal courts. But there is a narrowness to the legal profession (I'm a lawyer myself) that could use some tempering in the highest tribunal. It's a difficult point to make, exactly, but it's based on a recognition that if, as observed above, there is invariably a non-technical, political aspect to judging, then there is a place on the bench--in the minority, importantly--for judges guided by something else than professional expertise and the received traditions of the bar. It's not that they would be expected to ignore the law, but rather that their very amateurism might prompt fresh questions and novel approaches outside of the tunnel vision sometimes characteristic of certain types of professional experience and training.
Can non-lawyers make good judges? Of course they can. For about six years I practiced as a member of the Navajo Nation Bar Association. In the Navajo court system some, but not all, of the judges had law degrees. I could never really tell which did and which didn't. We argued to them, and briefed issues, as if they were lawyers, and the remarkable thing is, if a brief is done well, and clearly, it will be as intelligible to a layman as a lawyer. We are not dealing in matters arcane, like, say, quantum mechanics, but the everyday stuff of human interaction--the known and assumed rules of conduct, local custom, fairness, the need to restore harmony after certain balances are thrown off. Of course non-lawyers can make such judgments, and would give precedents and authorities the weight they deserve as a matter of fairness and respect for community standards. But they would also see things through their "lay eyes" that we with a particular type of training might miss. So, I would say, put 'em on (but no more than a third).
There is one other consideration. Maybe it's not so important that it goes in a re-written constitution, but there is something a little unseemly about Supreme Court judges hobnobbing with other high government officials whose actions they will undoubtedly have occasion to review. I don't think I'd cloister them, but I think it makes sense to to limit those kind of contacts, as we now forbid ex parte communications. The judges, after all, once were clerics, and a little more propriety, a little more independence, a few fewer duck hunting expeditions, would in all likelihood increase the respect for opinions rendered.
Conclusion: Dude, Where’s My Vote?
Yes, it is largely gone, because the lottery has taken over the job of finding representatives. It remains for choosing those with the job of electing the president, and presumably remains in State elections unless they too choose to overhaul the works.
It is a loss to be considered, but not without reflection on what a vote is for, and how often we cast it for less-than-creditable reasons, or in ignorance, or based on mere party enthusiasm, or in thrall to a carefully crafted advertising campaign.