Your other option is to just go east on Century @ Vicksburg on the ground level. This route is walked pretty frequently by passengers/crew staying in the closer hotels, such as the Hyatt. You can then make a left at Sepulveda or Vicksburg to go north.
As for drop-off, if your driver can get into Park One (aka Park 'N Fly) and out quickly, that's the closest. It used to be a 15-min grace period, but don't know if that still exists.