From what I have been able to find the Florida Championships was a tournament that began in the 1969-1970 season when the University of Florida added wrestling to their athletics. I believe it ended after Florida dropped wrestling after the 1978-1979 season. I was only able to find results from three tournaments though.
Miami-Dade (1) 1970
Florida (2) 1972, 1973
I want to say for Miami-Dade that I'm not for certain if the campus in Westview or if the campus in Kendall is the school to win the 1970 championship. To my understanding they both had athletics and they both had their own wrestling team.
If you have any more information regarding the Florida Championships please let me know.