Pappy, you're right, you need the Trail Crest exit permit.

They're like other wilderness permits at Inyo N.F: 60% (15) are reservable up to 6 months in advance, the other 10 (40%) are available on a walk-in basis. I think we are just past the 6-month window, so if you already know your exact dates, you should call right away and try to snag one of the reservable ones.