If you were in charge of a State GOP, what sort of primary system is best?

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The problem with jungle primaries is that it pushes the real action of the election to a low-turnout primary.

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I suppose I could see an argument against such a system, though, in that vote splitting could lead to a top two who don't actually get very much of the vote, and who might not be part of the top two absent vote splitting.

I think it's a good point that it would give people of the minority party a chance to have some buy-in, even if their own preferred candidate isn't on the ballot.

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I suppose I could see an argument against such a system, though, in that vote splitting could lead to a top two who don't actually get very much of the vote, and who might not be part of the top two absent vote splitting.

Right.  That's definitely a problem with run-offs, which is why IRV is better.  Though with many candidates and no party nomination, I guess that would be a lot of candidates to rank.

I wouldn't be opposed to something like a two-step jungle primary, where each party has its own process where the top two or three proceed to the free for all jungle primary, rather than everybody who can wrangle some signatures. But at that point, you'd be asking people to come out to vote three times for one election, which seems like it's bordering on onerous.