On one occasion, and this was for EPCOT, but same idea, we were FIFTEEN minutes late for EE opening. My boys waited in line for 1 1/2 hours to ride Test Track, I told them that this was not worth it anymore because this is what we'd hit all day, I took them out of there and went for opening of Typhoon Lagoon and got to do the Shark Reef over and over with no lines and enjoyed the relaxing rest of the day there.
Next time we did it right and got there 30 to 45 minutes before the gates open and avoided the lines and frustration!!! The key to taking advantage of EE day is to get there before the gates open and get ahead of the crowd, by the time the crowds get going, you've already got the crowded rides over and can finish up the morning doing the ones that are not as busy. I usually only hang around then til about noon and get out of there, by then we're ready for a swim break at the resort.