Have you thought about going through the Miter Basin and over Discovery Pinnacle to reach Mt. Whitney?
If you take this route you will be able to leave from cottonwood lakes th and return to cottonwood lakes th with same time period. I will be taking this route in September. Day 1 cottonwood th to High Lake #5. Day 2 over New Army pass to sky blue lake. Day 3 summit whitney & back to skyblue lake. Day 4 skyblue lake to high lake. Day 5 only 6 miles back to the car and a 4 hour drive home. Cutting through miter basin is shorter, more secluded, and very beautiful, from what I hear. Here is a link to a post on Miter Basin
Miter Basin/Crabtree Pass mrtbones