I like George's itinerary and as he mentioned you have a little extra time, For variety and acclimation I would go this way. My mileages are rough but all easy 1 day hikes with the exception of summit day and the last day but you'll be in great shape by then. On summit day you will only need to carry plenty of water and a day pack so not that bad.
Horseshoe to Long Lake - easy first day. About 6 miles.
Long lake to Rock Creek via New Army Pass - About 10 miles.
Rock Creek to Guitar Lake - about 10 miles.
Guitar to Whitney and back to Guitar - EARLY am start - about 10 - 12 miles
Guitar back to Rock Creek - 10 miles
Rock Creek back to Horseshoe Meadows via Cottonwood pass. 12 miles. Kind of boring but you'll be light and fast and at least get to see some different terrain.
I would prefer to exit via Whitney Portal but those trailcrest exit permits are hard to come by. If you threw in 1 extra day you could do a fine through hike by exiting at Kearsarge pass and Onion Valley. You just continue north from Guitar on the JMT. Camping spots would be Tyndal creek, Vidette Meadows and out. Be 3 10 mile days through some pretty awesome scenery.
