The exit date is really between you and your family, not the government. They are not going to report you missing unless you are late.
The exit permit idea is bureaucratic stupidity. If it puts 4 or 5 extra people on MMWT one day, 4 or 5 less the next...who cares other than the bureaucrat? Issue 25 entry permits per day with a Whitney Zone enhancement, the rest will take care of itself.