I was able to snag an Ohana breakfast for the 15 of August, just a week and a half ago. We ended up cancelling a dinner during the week, and had a TS credit left over, so we are going the morning of our check out date.
So, even during a busy time, I got one.
Granted, it is the day we are leaving, at 855 am, and we are not rushing to get to a park, but when I went to book, they had 3 times available, all before 1030 am.