Thanks for the shuttle suggestions. I didn't now they offer private shuttles as well. I assumed it was always a shared ride and then the math doesn't make sense.
How does it work if you use, e.g. Prime Time, as a private shuttle for 5 people. Is someone waiting for you with a sign at baggage claim?
ExecuCar's shuttle said max 4 people but I will call to see if the will allows 3 adults + 2 small kids as well (picture of the van looks like we should all fit).