Which methods should be used to select major party presidential nominees?

The 2020 presidential campaign is on. At this point, we don't really know either who will win the Democratic nomination, or what will happen in the general election. So it's as good a time as any to consider what methods should be used to select major-party presidential nominees.

I'm going to assume that :

1. both parties will use the same process
2. we will in fact continue to have just two major parties.

I recognise that many will disagree with one or both assumptions, but they do help focus the discussion. Similarly, I'm going to focus only who WHO gets to pick the nominee, though I recognise there is also disagreement about various procedural aspects of the process. So, which of the following methods do you prefer:

1. Open primaries: Any eligible voters gets to vote in whichever primary he or she wants (this is how most primaries work today).

2. "Closed" primaries: Only registered members of the party in question get to vote.

3. A convention of dues-paying party members: This is how the biggest Canadian political parties choose their leaders.

4. Party elites making decisions in the proverbial "smoke-filled room" (the method used throughout much of American history). Today, there probably wouldn't be much actual smoke, as most political elites don't smoke any more. But you get the idea.

5. An epistocratic approach: Only party members with a certain level of education and/or political knowledge get to participate. Or, alternatively, those with greater education and/or knowledge get "extra" votes.

6. A hybrid system: Ordinary voters get to participate, as per option 1 and/or 2 above. But party leaders get a disproportionate role in the process (e.g. - they get to prescreen candidates, they can veto them after the fact, etc.).

7. The nomination will be decided by gladiatorial combat.

OK, I was kidding about that last one. But all the other six options have actually been used at some point in US history, or that of other democracies, and/or have been advocated by political theorists. Which do you prefer, and why.