The first line of wikipedia for liberalism is: "Liberalism is a political and moral philosophy based on the rights of the individual, liberty, consent of the governed and equality before the law. Liberals espouse a wide array of views depending on their understanding of these principles, but they generally support individual rights (including civil rights and human rights), liberal democracy, secularism, rule of law, economic and political freedom, freedom of speech, freedom of the press, freedom of religion, private property and a market economy."
I sincerely hope that is something we can come together and agree are important in the US. Even though it sounds like you and me have very different political views it also sounds like we agree that all of these are good. That means we have a wide array of items we agree on, but that are in danger at the moment. It seems to me there is a common platform most of us could agree to, but both parties have been to some degree hijacked by extremist so both of us to some extent are supporting illiberal candidates when we really don't agree with that.
Which is also not much of a home, since it generally is inhabited by non-serious people- but at this point at least I can morally live with a platform of you stay out of my way and I'll stay out of yours. The other options have too many compromises right now.
Replacing FPTP with RCV would elect more centrists, but without proportional representation there'd still be two parties I think.
I think the problem is not that the parties are too strong, but that are too weak to strong interest groups.