That doesn't work in FLA, here you must be registered as a Republican to vote in the Republican primary, a Democrat for the Democrat primary and so on. As there are so few NPA, I, L and GP candidates for state and local offices the so called independents are shut out of all but the general elections.
Here it's better to register as either a R or a D and then vote split ticket in the general elections.
As screwed up as FLA is when it comes to voting many states are even worse.
Kentucky is the same way, you have to be either a Republican or Democrat in order to vote in primaries.