This happened to me a few months ago. I kept trying until 12:30 am, went to sleep, then logged in at 7:30 am and got boarding group 8.
I am not sure whether I would prefer to start at 8 am ET and keep trying to log in for several hours. That would be worse for people in the western part of the US, who would wake up early and debate whether to go back to sleep or keep trying.
What would be better, clearly, is for Disney to get their websites routinely working properly.