When looking at permit options for my own hike this summer, it appeared that the best way to get a walk-in exit permit was to have the longest possible hike duration - the exit pass is very rare for a walk-in pass in that it is being issued for many days in advance, but can only be issued in conjunction with a current (or next?) day entry permit. So in theory you could be first in line on 30th July but find that the exit permits for 4th August were all issued a few days earlier to people on longer hikes.
When I collected my permit last year the rangers were very clear with me that exit permit dates had some flexibility; if you came out +/- a day it didn't matter at all. I was upfront that I would be exiting a day earlier than my permit and they really didn't care.
