Early departures back to U.S.

Renting a room at the airport hotel is the best option we have found.

Next best option: sleep in the airport. I and my daughter did it in Geneva. It's safe--you're locked in from midnight to 5am, and we slept right across from the airport police office. Yes, it's for the more adventurous traveler. With an air mattress or sleep mat, it's comfy on the floor.
All the details can be found at www.sleepinginairports.net

This is one situation where I don't prefer a nonstop flight, but rather a later departure with a stopover.

When doing a flight search on Kayak, on the left side you can keep clicking "more options" (or something like that) and choose departure times of flight 1 and flight 2. Your Geneva to Atlanta flight is flight 2; move the slider to something after 10 or 11 AM, and see what comes up.

For that early I prefer a hotel at the airport - just makes things easier.

Although I do not normally fly Delta, a few days ago they were offering flights from Geneva for more than 50% less than other carriers. I booked their 10:30am flight departing Geneva with a connection through Paris. The flight is operated by Air France as Delta partners with them. There is a strike alert posted on Air France website but I don't usually worry about it unless it happens, then I work around it. As far as a hotel, not long ago I was placed at the Movenpick Hotel by my airline when my flight was cancelled and it was excellent. They are not located directly at the airport but they offered a shuttle. I don't remember what time their shuttle service started so that would be worth an inquiry before booking. Another option is to fly from Zurich as they may have direct flights to Atlanta.
I agree with the other advisor who recommended you put your desired departure times in Kayak. There may be better options available as well.

Hi travellers,

I've been losing sleep trying to figure this one out! Thanks SO much for your alternatives. Really want to see the Alps, so I'll make this happen.

Happy future travels!