The first time I went up Whitney, it wasn't even planned. The reason being, it was the Labor Day weekend, and I thought it would be full. I was going to do Langley, but stopped by to check the day before just for the heck of it. Turns out, I was the third name drawn in the "raffle" at the visitors' center, and the rest is history.
You should have a good chance if I can get something on the Labor Day weekend. As others have said, Langley is another 14er with +20 miles of hiking and should give you a good challenge as well.
