A little late to this discussion so I may have misread some points:
I think people underestimate just how politically "efficient" America's current political coalitions already are. If anything, the two parties have only gotten more efficient at sorting the electorate over time (i.e. Hyde Amendment), and that's what's created the hyperpolarized political environment we're currently in. The fact that there's no overlap between the two parties should be a sign our democracy is working as intended.
Can also look at things like fusion party labels - the third party labels never cross over (i.e. a conservative third party endorsing a Dem/liberal or vice versa) unless they're running in an uncontested race. Lots of reasons why this can be the case (fundraising, party machines, etc.), but you'd imagine that largely pre-sorted ideology has to be a large factor in this. (Once upon a time I wrote my thesis on fusion party labels as potential solution for hyper-polarization, was not heartened by the results. Admittedly it's been a few years...)
The issue is less about how we vote, and more about how we legislate from the coalitions that already exist - and would exist regardless of how we formed our political parties. How would the ideological coalitions we form be any different? I don't buy regionalized parties in the U.S. at all - not in an era of TV and internet.
The system isn't broken, it's the electorate that's broken. In any political system driven by incentives, the only way to prevent rulebreaking is to punish it. The electorate has yet to punish the GOP post-1994.
That would break any democracy - the United States isn't unique in that respect.
