Tuckster, have you considered the van service that Amtrak provides to area hotels?
The Amtrak System Timetable says, "Orlando Hotels and Attractions: Coach USA provides door-to-door shuttle van service between Amtrak's Orlando station and Orlando-area hotels and attractions. Vans meet the arrivals and departures of all Amtrak trains at Orlando. Arrangements may be made in advance by calling 407-826-9999, or with a Coach USA representative at the Orlando station upon your arrival by train."
We considered this option for a trip this past December. For 2-adults and 2-children, from Orlando Amtrak station to AKL the quoted total price one-way was $35. We needed a car though, so we rented from Hertz at the Amtrak counter at the Orlando Amtrak station.
Maybe someone who has used this service can give you a first hand report. You should check the latest Amtrak timetable or talk to an Amtrak representative for any changes to this arrangement.
Good Luck,
LittleBear