lawnerd, if you have an overnight permit, it is good for up to 14 days. You do NOT need to exit the date declared on your reservation or on your permit. They do like to record your planned exit date so they might have an idea whether to start looking for you if you are reported missing. And possibly for statistical purposes.
The only place an "exit" date is required is those people hiking out the MMWT (main Mt Whitney trail), who have started on another trail within the Inyo National Forest. They imposed a quota of 25 per day on those permits after they found a large number of people were coming in from Horseshoe Meadows and Onion Valley to climb Whitney and exit the MMWT.
As for driving home on summit day -- I have often done that, and my drive is farther than yours. I find I am especially charged up after a good day on the mountain, and my body is very happy to sit in a comfortable bucket seat and do nothing for hours after all that exercise.
