Well Andy, I just couldn't help myself, and I called the WP number myself. I learned...
1. They can't adjust your dates online, same as you.
2. Your best option is to hope for a walk-in TC Exit permit for your target exit date when you go in to pick up the permit. As Hobbes points out, there are 10 walk-in exit permits available starting out, and your target date could only be reserved by people picking up their permit the days before you do -- those entering on a trail head farther north than yours. You have a very good chance of picking up your desired exit.
3. Another option: Since you are coming for so long a trip, you could possibly exit at Kearsarge Pass/Onion Valley/Independence for a resupply, and then start a New trip on that trail, and pick up the exit permit for that trip, since that part only takes 3-5 days.
4. Also as Hobbes pointed out: plan your trip for a Cottonwood Pass/Horseshoe Meadows exit (carrying 1-2 days extra food), and then when you pick up the permit, see if the Exit date you want is available. Actually, to use this option, you don't even need to revise your existing Aug 14-20 permit, since the entry date is the only hard-and-fast rule. Exits can be anywhere and any date (except for the Trail Crest option.) They just want you to give your best estimates of camping locations and exit when you pick-up the permit.
5. And a last option, that Hobbes or I could take: Exit off the Whitney summit via the Easy Walk-off (only easy in summer, deadly with snow/ice), down the Mountaineers Route and the North Fork Lone Pine Creek. No exit permit required. If you are experienced with off-trail travel, we can help you navigate this.
All good advice except for #5. The MR descent is class III with non-trivial navigation and serious hazards in several places, such as rock fall and exposed sections with a possibility of a deadly fall. Not for hikers w/o proven mountaineering experience.