We did AK twice - on an EE Monday and on a Saturday. I would highly recommend the Saturday! It is not worth your time to go on EE day but Saturday was great.
We stayed the whole day and didn't find it too crowded - even in the middle of the day. We had fastpasses for the Kilamanjaro Safaris and we didn't need them! It was a walk on at 3:ish. Of course it was raining but we didn't care.