I think your best bet is to go with SuperShuttle. We had a return flight leaving around 8 AM (departure from John Wayne, however). We called them just the night before to make a reservation, and requested a pick up time of 5:30. They told us it would show up between 5:25 and 5:40. The van actually got there at 5:30. The only thing you should know is you can possibly make multiple stops at other hotels before reaching the airport, so give yourself plenty of time when deciding on a pick up time. Better to show up early at LAX than racing to catch your flight!
The front desk staff at HoJo also recommended Jag Transportation. It's a towncar service, with private driver. They always showed up before schedule when we went to Knotts Berry Farm or nearby attractions, and the service was courteous and very professional. They usually offer a flat rate... it's a little expensive, but it gives you incredible peace of mind.
Hope this helps!
I know you'll enjoy your trip!