The Trail Crest exit permit is designed to keep too many people from circumnavigating and coming down the main trail. As long as you have it, I understand the rangers are not too particular about whether you exit on the exact date. And I'm pretty sure it is the upper section that they would be most concerned with. You would have no problem camping an extra night at Outpost Camp or Lone Pine Lake.
All other permits do not require you to be off the trail by the stated date. So this one should not be a problem.
I tried hitching to Horseshoe Meadow in the afternoon because I'd left my car there. The traffic is sparse, so way more difficult than getting up or down to/from Whitney Portal. Hitching a ride up in the morning would probably be easier due to more traffic. (That was the time a fire broke out up there, and my car was stranded behind the closed road for 4 days. What a pain that was!)
