We are spending 3 nights at the Grand Californian in Aug
Our fight home from LAX is really early and we thought it would be less stressful to stay at an airport hotel the night before and use their shuttle over in the am to catch our flight. I am not sure of the best way to get from Disney to the airport hotel. SuperShuttle and Primetime look as if they only go to the actual airport?
Taxi or one of those limo companies?

Our fight home from LAX is really early and we thought it would be less stressful to stay at an airport hotel the night before and use their shuttle over in the am to catch our flight. I am not sure of the best way to get from Disney to the airport hotel. SuperShuttle and Primetime look as if they only go to the actual airport?

Taxi or one of those limo companies?