I do not think it will be the doomsday scenario everyone here is making it out to be. If Nemo opens June 11 then there will be 2 1/2 weeks there before the AP blackout begins. That will spread AP holders out over that time. Plus the folks with EE will have a huge advantage over the AP holders on EE days because you can either ride Nemo during EE (if DL does this) or get in line for Nemo before the AP holders can get into the parks.
The 45-60 minute comment was about a Sunday in June - days that are non-blackout days. The Sundays will be worst for AP holders squatting on the Nemo ride, and there is no EE on Sundays. It is best to avoid Nemo (and possibly DL altogether) on those two Sundays (June 17 and 24). Also, the first couple days - June 11, 12, etc., will also be pretty busy for the Nemo ride. If you want to ride it those days, get there early. As it gets closer to the end of the month I think it will settle down somewhat, especially on weekdays.
Personally, I would rather have gone in August this summer, but we have the other trip I told you about in June which dictated the DLR visit for the last week of June. So we will do our best. We only have three days, and I am hoping we can ride Nemo twice. We'll see.