Welcome, easy! Actually, your plan "A" should be to try for walk-in permits for Mt Whitney! There are quite a few cancellations and no-shows, and their permits do become available. Check the
Unused Permits 2012 page. If you walk into the Visitor Center about 8:30 the day before you want to hike, you are likely to get permits from people dropping a person or two from their reservations, as they pick up permits.
Then on the day OF the hike, at 11 AM, the no-shows are made available for overnight backpacker permits. Day hike permits are a little different, but it is all described in the "Wilderness Permit Options" (link to the left) in Step 6.
As for Langley, the Cottonwood Lakes quota is 60, with 24 reserved for walk-ins, which become available at 11 AM the day BEFORE your hike starts.
So, I'd try for A. walk-in permits for Mt Whitney, B. walk-in permits for Mt Langley, and C. White Mountain.
If you try for A at 8:30 (and every half-hour after that) the day before, and then B at 11:00, it is unlikely you will be skunked.
And one more thing: In the two weeks before you arrive, set up a bookmark to check the
July permit availability for Mt Whitney for that week,and check it often, a few good people will log in and release their reservations if they decide not to go. So you might get a reservation that way.