Some airlines allow you to check in your bag the night before at ZRH. Here is some further information - in German, unfortunately (that's just where I ended up!). The "ja" and "nein" refer to online check-in, the instructions on the site say that you should click on the name of the airline to find out more.

http://www.flughafen-zuerich.ch/desk...spx/tabid-113/

If you airline allows you to drop off your bag the night before then life is going to be a whole lot easier for you... just drop off everything the evening before except for an overnight bag.

And for a 7 am departure I would definitely recommend the Radisson Blu in the terminal building, if you can get an affordable price.