> I don't believe that fixing those problems would solve the underlying issue, which is that the voters themselves have a deep antipathy towards each other.

The evidence is very strong that the reduction of the dimensionality of discourse and the polarization are a direct result of those features of the electoral system.

> I'm hard pressed for a solution short of starting over from scratch,

That's not only not a solution, it is not even an actual option. You can't start from anywhere except where you are.