So this FedEx Day sounds like asking your staff to work 24 hours straight on a company project in order to boost morale... am I being cynical in thinking that this might have the opposite effect?
You aren't asking this, and that's quite the cynical view.
Companies take a day off from work. I think the original one was 3pm Thur-4pm Fri. Teams self-organize, and they have that period to see what they can accomplish and get done. Some do work longer hours, some don't, but they try to get done what they can in the time allotted. There isn't any agenda or milestone. Teams set their own goals, going as far as they can.