OP: I agree with everything you got as an answer, the only thing I'd like to add (since you are traveling in the peak of the peak season in Europe) is that you should be prepared for a rather long walk in ATH, and crowds of people hindering you. Keep in mind that as a business passenger, you'll go through the fast lane at security, and you'll have to scan your BC for this. Good luck!

PS I just realized that you'll be arriving in Athens at 5 am. Good, there will be fewer people in all the queues!