First of all, LAX, the airport, is not a horrible place. And leaving from the Bradley (International Terminal) between 11pm and 6 am is pretty pleasant and not stressful at all. I've done it at least a half-dozen times on flights to Asia.
BUT you are cutting things very, very close assuming that the CS is on time into Los Angeles. If the train is even only a half-hour late, that puts you on the 10 pm Flyaway to LAX. The Flyaway uses HOV lanes for almost all of its route to LAX, but with even a little traffic congestion along the route, you won't get to the ticket counter until close to 11 p.m. If the train is more than a half hour delayed, you would be pretty much out of luck, considering you are taking an international flight.
One alternative could be to detrain at Van Nuys, in the San Fernando Valley, where the train would stop, if on time, at 8:05 pm. The Flyaway also runs every half hour between Van Nuys Amtrak/Metrolink and LAX, taking about 45 minutes. So you could catch the 8:30 Flyaway and be at LAX by 9 p.m. at the latest. With even an hour delay into Van Nuys, you would be on the 9:30 pm Flyaway and at LAX by 10:30, even with congestion, and still have plenty of time for your flight.
So it seems that you have to weigh the odds of the CS being more than 75 minutes late into Van Nuys versus having to take the rather pedestrian (compared to the CS) San Joaquin train/bus combo.
Good luck!