People often say that the earlier in your trip you use it, the better... the reasoning goes that as your trip goes on, you get more worn out, and getting up early gets harder. I can attest to this; we were staying onsite so had an EE on our second day (Tuesday) and two days later on our 4th day (Thursday). Thursday was a lot harder to wake up for! We were so tired by then.
Also seems like you'd get more use out of it on a weekend day. That would be when the crowds are expected to be worse. For the MM you're not eligible for, you could just start on the left side with Adventureland, along with everybody else at rope drop.