I've been building a world set in the near future (decades/centuries) that includes Florida as an island. My intent was for a manmade or natural event to occur at or near the South Georgia Rift, but I can't seem to find anything capable of creating that much force that wouldn't also cause apocalyptic damage far beyond the region.
Not very easily. Or not in the way you (I think would want to). Florida is not flat. Miami is just around 16 ft above the sea level while Tallahassee is 190 ft. So rising water level would flood the penisula part first rather then closing gap beetwen Gulf and Ocean.
But there is a belt, coming from Spring Hills, Dunnellon to Ocala, Palatka and ending In St. Augustine. It's land beetwen two rised patches of land. On the Palm Coast it's also very damp and with Saint John river. So you could use this to flood Jacksonville and turn additional water to move it toward the gulf.
Soemthing like this
Keep in mind that this would need to be 99% man made. Any natural occurence in rised sea level would result in floodin Miami, Fort Myers and Tampa.
Here is a projection of Florida with sea level rise.
Maybe your future people avoided this by excavating out the peninsula at about the level of Daytona Beach and moving the fill to Miami to keep it above sea level?