There are other agencies which service LAX transit center:
S.M. BigBlueBus
http://www.bigbluebus.com/home/index.asp
Culver City (big green) Bus
http://www.culvercity.org/depts_bus.asp
Have you tried the Thrifty rental car shuttle? It's not too hard to sneak in there!
Also, don't hesitate to haggle with a flagged-down cab who is heading to the LAX taxi queue anyways.