In July, I did pretty much the same trip that you're thinking of doing. I had a 6 day permit, to allow for maybe needing an extra day due to altitude or whatever, although I planned the actual hiking portion of the trip for 5 days. Here's what I did:
Day -1: Camped at Whitney Portal after traveling all day to get from New England to Lone Pine.
Day 0: Got permit, last minute shopping, picked up box of gear at Post Office, etc. in Lone Pine and camped at Cottonwood Lakes Trailhead. No permit needed, but there is a self-registration drop box with envelopes for the fee.
Day 1: Hiked to Rock Creek
Day 2: Hiked to Crabtree Meadows
Day 3: Summit and back to Crabtree Meadows
Day 4: Hiked from Crabtree Meadows to near the Siberian Pass/New Army Pass Trail junction.
Day 5: Hiked back out over New Army Pass to car.
I definitely had a shorter day on Day 2, and could have gone up to Guitar Lake or higher. Since I was coming back the same way and not exiting down to Whitney Portal, it really didn't matter and saved me from hauling gear some extra miles. I was also able to relax more before summit day.
The only problem I had with acclimating was the loss of appetite. I was aware of that, so I just made sure I was eating regularly.
There are lots of different ways to divide up this hike and many places to camp depending on how you are feeling/weather/etc.
