Um, have you tried calling any taxi companies directly and asking them what their pick up/drop off procedure is for trips to LAX? My guess would be that they work like the shuttle companies. You tell them what time your flight is or what time you want to be at the airport and they schedule a time to pick you up. Beverly Hills Cab comes to mind immediately. I'm sure that the cab companies have a system worked out as it won't be the first time that they've taken reservations for passengers needing to be at the airport at a certain time. I just wouldn't book or make a reservation too far in advance.