Florida actually was really red in national politics during the 1970s and 1980s, though the Democrats continued to control the state government. If you check the elections during that period, except for the anomalous election of 1976, Republican presidential candidates consistently ran 5% to 10% ahead of their national popular vote percentages in Florida.
The key to understanding late twentieth and early twenty-first century Florida politics is that in federal politics, the state pretty much votes the way the latest group of people to move there has been voting. In the 1970s and the 1980s, it wasn't just the Cubans, it was conservative midwesterners. Alot of the recent tilt back to the Democrats, though its still a Republian leaning state, is due to the Puerto Ricans.
You really just have to have alot of Republican voters move to Florida from other parts of the country to make Florida red. For some help, you can have the Russian Jewish emigres go to Florida instead of New York, in New York their votes get drowned out in in Florida they could strengthen the Republican edge.
Another factor in Florida politics, and something that could happen in Texas and keep Texas more of a swing state, is that the Democrats managed a series of really good governors that kept the party as a credible factor in Florida politics. The Republican governors weren't as impressive when they started being elected. Much of this depends on the personalities involved, though it would take multiple small PODs.