As an NPA, I’m pretty much disenfranchised from making much of a statement in Leon County primaries. While I think making Florida an Open Primary state would be worth trying, that process also has it’s shortcomings.
A colleague in a northern state with Open Primaries, a staunch liberal, voted for Trump in the 2016 primary! Because he thought Clinton would have the best chance of winning in November if Trump was her opponent. Then he voted for Clinton in the general, of course.
That scheme didn’t work out too well for him.
Meanwhile, the biggest change Leon County needs to make is to eliminate the At-Large districting. This is nothing but a scheme by the libs to block any chance of getting a conservative into city or county commissions, because there are significantly more D’s registered in the county than R’s.

No, Dave, that’s not what we do. Currently, we have multiple primaries on the same day. Usually, it’s just two: One for Rs and one for Ds; we could have more if other parties had more than one candidate, but I’ve never heard of that happening. The primaries may be held on the same day, but they are different primaries with different ballots; they are partisan primaries. The winner of each party’s primary advances to the runoff (i.e., general election). I prefer to see a single primary where every candidate is listed on the same ballot, regardless of political affiliation (i.e., a non-partisan primary; you may be able to list each candidate’s party preference, but all candidates appear on one ballot). The two candidates receiving the highest number of votes in the primary advance to the runoff (i.e, the general election).

That’s what we do NOW. Everyone runs in the Primary (except the Offices with only 1 or 2 people running) and the two people with the Highest Votes in each category move on to the General Election. The only difference between your idea and what we actually do is, you call your Second Voting Event a “Run Off” instead of a “General Election”.