As a college All-American who had my long run every damn Saturday at 6:00 am..... Take a multivitamin with a glass of water and an electrolyte pill. You tend to pee out all your water soluable vitamins while drunk as well as sodium ( duh, we know that) . I have had some of the best long runs of my life hungover. It's a weird phenomenon. Maybe it was the guilt? Who knows.
I never had a Sunday long run when I wasn't hungover. I don't see the problem. Aren't the other guys you're running with going to be hungover too? If not, you need to start inviting them out on every Saturday night and make sure they drink more than you (this is the obvious solution by the way).
With references to Euros in your post, is there any chance you have access to Irn Bru? That might help...