There IS another option not mentioned yet: Hike from Horseshoe Meadows, over New Army Pass or Cottonwood Pass, and then north on the PCT to Crabtree Meadows.

Then, climb Whitney from the west. You could probably do it in 3 - 5 days, depending on your hiking speed. By the time you got to Mt Whitney, you would certainly be well acclimated.

Permits are fairly easy for this route, but you would need the TrailCrest Exit permit to go out the main Mt Whitney trail.