Lysis -- South Florida tornadoes have a number of origins, almost all of them equally likely: weak tornadoes from daytime convection, tornadoes with squall lines/cold fronts in the overnight hours, tornadoes from tropical cyclones, and so on. I imagine it's the relative equality of the first two factors that plays the largest role and not really tropical convection, which isn't generally associated with tornadoes (tropical cyclones being the exception, but only as they make landfall and interact with the midlatitude weather pattern).

Converging winds are found in a lot of places in the tropics, not just tropical cyclones. As mentioned, you can find them along the ITCZ or with tropical waves, but two other examples. There exist others on smaller scales.