The Visitor Center in Lone Pine will give you the option to pick up the permit in the night box -- in the kiosk by the road.
I think that requires that you not camp in Sequoia N.P. (not sure about just hiking into the park), but you can alter your itinerary if that is a kink.
Call the Wilderness Permit office in Bishop: 760-873-2483 and figure out what is required. They're the ones to call to set up the night-pickup.
I'd go OAP -- dawn would likely be approaching by the time you got to the upper half where any difficulty might be.
