First, thanks for an intelligent essay on an important topic.
I agree with those who think that the existence of political parties is the biggest, nastiest ‘fly in the ointment’, as people used to sometimes say. One possibility for removing political parties would be to have a single political party, at least at the national level.
Sure, 'single-party states' have historically been associated with authoritarian (and worse) regimes, but that does not mean that has to be the case. In this proposal any (adult) citizen would be free to join — or leave — the party (any number of times), which would cost nothing to join. Citizens who were not members of the party would still have the right to vote, etc.
In this proposal there would be caucuses within the party that would in a sense be 'parties within the party'. Howsoever, they would presumably limit themselves to a particular focus (such as the environment) or perspective (evangelicals might form a caucus) and, unlike the political parties that now exist, people could conceivably join more than one caucus (though caucuses would be free to bar people who were members of any other caucus, if that’s how they wanted to be).
As conceived, the only official function of caucuses would be to nominate candidates for elective national offices (President, Senate, Congress). A person would have to be a member of the party to be nominated for office.
if curious for more: “An Alternative to Volek’s ‘Tiered Democracy’” (here in Medium, but not behind the paywall)