You don’t have to. Collect your eggs daily, and no chicks develop. If you get a broody, break the broodiness, and no chicks. As you can see, it’s pretty easy to avoid having chicks.
They’ll be fine. I don’t know the winter temperatures in Florida, but It can’t be that cold. The chicks will be fully feathered by then and fully able to handle cooler temps.
If the other hens have access to her, I’d mark the ones she’s sitting on and check the nest daily to remove any contributions to the nest. I draw a circle around the egg with a black Sharpie, and once a day I go out, lift the broody up a little with one hand, look quickly and remove any...