drop rental, use cart for big bags then check in.
I the old days, you could drop off people and bags at DEPARTURE curb side, then go drop off car, meet fan ly at the Tix gate for a flight. NOW, that's not effective at TIA. All the rental car drop off spots are prepared for big / lots of bags. Tourist in Florida is a thing we know. Drop off the car then bags go with you to Tix counter. Leave extra time for car drop off, sometimes they are busy too.
Drop your rental car first, then you can take the train to baggage check.
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