Try getting the Southwest credit card w/ 50K bonus points for travel from NYC area to Florida.
Otherwise, UA is probably better to bet on availability these days over AA.
Also if you can drive/train down to PHL sometimes they have availability out of PHL to MIA on AA that you can't get out of EWR/LGA/JFK. I don't know where you want to go in Florida but if it is MCO then check the JFK to TPA route as well.