If BG don’t stick around for a more reasonable amount of time in the mornings once the crowds go, I think it would be almost better to move to a full on lottery system that could be accessed from anywhere. Ration the amount of times a person can enter per period of time, set rules around who can enter (a hotel check in date, a ticket linked for the appropriate dates, an AP that hasn’t won the lottery for the appropriate amount of time) whatever it takes to make it work.
Obviously that comes with many flaws, most notably the higher amount of people who would enter without the barrier to entry, but its not okay that someone can waste an entire day at Disney, arriving exactly when they should be very early in the morning, and not get to ride. It is a lottery at this point, but with a fairly high cost to enter. Maybe it would just be better at this point to lower that entry cost.