For the exit permit, it is the day you start descending from Trail Crest, as if Trail Crest were the trail head. Though we have heard rangers are flexible on this -- day before/after is ok, just HAVE the exit permits.

The out-and-back would be to enter at Horseshoe Meadows, and use the PCT, maybe return over Army Pass. I am pretty sure you are going to get all the permits you need, though. See the following...

Last night I played on recreation.gov and found that the exit permits available in the 6 month window move to the next day at 9 PM sharp. (That's midnight Eastern time, where the Rec.gov website "lives".) So if you want to be sure and grab the permits you need, you can practice the process before the night when the ones you actually want become available. Practice makes perfect, and if you do that, you can grab the permits maybe 5 seconds after they pop up.

You can set up the screen (here's the Aug 5-18 window) ...but practice using a current window that shows several "X=not available" dates on the right, with mostly available dates across the 14-day span.

At 8:59 PM... Make sure you are signed-in, set your group size correctly, and have the entry date for Kearsarge already set. (Note that if you select your Kearsarge date, it turns gold, then if you Update Availability on that section, the selected date shifts to the left side of the 2-week range.)

Practice repeatedly clicking the "Update Availability" on the exit permit section, so you catch the event of the next date opening.

By repeatedly clicking "Update Availability" on the Exit Permits, you can catch it as soon as the date opens. Once it does, quickly click the "A" to select that date, scroll to the bottom, and click the Book Permit button. The time it takes you to click, scroll down, and click is all you need to grab your permits. You then have 15 minutes to complete and pay for the permits. Nobody else can get the permits during that 15 minutes.

In that 15 minutes, you have to fill in the overnight spots and pay. The overnight spots can be anything in their list--you can change them later, just select anything. "Other/Don't Know" works for all but the first night. Don't forget to enter "Foot" in the Travel Method, and check the "Yes I have read..." box at the bottom. You can go all the way to "Complete this purchase" in your practice session, to make sure you understand all the steps.

Practice this several times a couple of nights before your exit date actually opens. ...I had all 15 exit slots tied up last night for a while. :-)