If you don't like the LAX-itive solution, there is a simple way to speed your trip. Walk to Sepulveda and Century. It's 4 minutes from Terminal 1. From there you can catch a city bus or hail a ride without delay. Take the LA 232 bus south, LA 117 east, or Torrance 8 bus southeast.
I predict this option will become so popular that bureaucrats will kill it within 6 months.