The dominate political party in Florida during the 1960s were the Rats. There was one GOP governor - Claude Kirk during that time period. GOP majorities in the legislature didn’t really appear until the 2000s.
https://en.wikipedia.org/wiki/Political_party_strength_in_Florida
Quote
There was one GOP governor - Claude Kirk during that time period.
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Reedy Creek:
Enacted by
Florida Legislature, 1967
Enacted
May 12, 1967
Signed by
Claude R. Kirk, Jr.
The bill, which was sought by and pushed for by Disney,[5] was signed into law by Florida Governor Claude R. Kirk, Jr. on May 12, 1967..
Only one GOP governor.
It appears all it took was that one GOP governor you referenced..