I may have misunderstood your plans. You need the Trail Crest exit permit if you start at any trail in Inyo National Forest, and then descend via the MMWT (Main Mt Whitney Trail) to Whitney Portal. I thought that is what you had planned with the loop trip.
However, if you start at Horseshoe Meadows, go to the Mt Whitney summit, and then return to the same trail head, (or any trail other than the MMWT), you don't need that exit permit.
But you are going very late in the season, so those exit permits should also be available.
