I like the idea of weighted representation, though I think you'd have to take at least the top two to avoid disenfranchising a significant fraction of the population under a winner-take-all approach, given our two-party politics. Taking the top 3 might make things interesting. You could imagine the dominant party's candidates finishing 1st and 4th, for instance, resulting in the minority party having more representation than the majority.

If the party finishing 2nd and 3rd had more votes than the party finishing 1st and 4th, they wouldn't be the minority party. I find it more likely that the 3rd and 4th places would be taken by third parties, and you'd have something like this:

1st: Republican

2nd: Democrat

3rd: Green

4th: Libertarian

...in which case the Dems would be the minority party, but the left in general would still hold a majority of the votes (assuming 2nd + 3rd > 1st + 4th).

If I may offer my opinion as an outsider from the EU: something like this may actually open up the traditional Left vs Right spectrum to something that is more closely resembles the existing diversity of opinions and values. For instance, here in Germany, these days coalitions between 2-3 parties is the rule rather than the exception. An interesting side effect of this has been that issues which at any given time were not the focus of the major parties can still be addressed by the smaller (often junior) party of the ruling coalition, e.g. the Green party who pushed the topic of environmental protection as a junior coalition member already in the late 90s/early 2000s.

Not true. The top vote getter might siphon off enough votes from their party's second place finisher that it drops them to fourth overall. Some of the voters will have "wasted" their vote on the party leader who would've been elected anyway even if they voted for the next highest party candidate. Think of two parties splitting the vote 60/40 overall. One party's votes are split 45/15, the other's 20/20. In a "top 3" scenario, the minority party gets two spots to the majority party's one.

Why encourage those who cannot prioritize making their minds up against a common enemy? Effectively, this scheme looks to empower any majority no matter how comprised. Clarity of purpose should matter.

The funny thing about "should" statements is that we get to disagree on them without justification. I see no reason clarity of purpose across multiple humans should matter, nor any reason that people should be corralled into picking between two corrupt options.

Clarity allows governance. Otherwise we're just reacting.

Hopefully a number within reason. I could see some states protesting congressional salaries by having thousands of representatives.

Surely the salaries are also divided up in this scheme...

That seems like a reasonable solution. Perhaps if a state with a high representatives-per-constituent ratio wanted their representatives to be paid well, they could make up the difference out of their own budget.