This forum gets a lot of "I have a 6 AM flight from "x" airport ... what can I do?" questions every week.
Here is a suggestion of how avoid the early, early departure problem.
Research the non stop, direct to the USA flight options first. It has been my observation that a majority of the american carrier flight's back to the USA from many if not most European cities leave between 10 am and 2 PM. They have flown in from the USA with an early morning arrival 6 AM to 10 AM. The airlines service the plane and are ready to return to the US in 2 - 4 hours after their arrival in Europe. So none of these flights are going to give you a 6 am departure and the problem of getting to the airport at that time of the morning.
A low hassle trip to the airport after a somewhat normal night's sleep should allow you a lower stress return flight and could make a better end to your vacation.
After viewing the return flight options then you can choose the US departure that has the best time and price for you. This works for open jaw flight plans also.
It doesn't always work out price wise but at some point better flights and more convience can be worth a little more cost.
P.S. Has anyone else been enjoying the scenic aerial shots during the TV coverage of the Tour de France on the Versus Cable channel. It can get your travelin' fever up!