With 6, you may not fit in one taxi or towncar. A full size limo could be expensive. Mears charges per person, which will add up. You may want to look at renting a mini-van, National/Alamo has a drop-off at the Dolphin if you don't want to keep it for the whole trip.
You should be able to get a taxi van at the airport. There are lots of larger families that need them. You may even be able to book a car service that has a large suv or van.