You could also try flying into Tampa (TPA) and catch the AA flight from there. You still have to go through MIA but it would be as a connection so no driving between airports (and cost of a car rental/taxi). Tampa is a much better airport for customs ect than MIA or FLL. You could even look into flying into MCO and then AA from there.

AA also flies nonstop from ORD to CUN.

You don't say where you are flying FROM so hard to know.