AAL is a pretty small airport, there should be no problem in walking around to departures for the standard turn time. Buy two tickets, do online check-in before departure from CPH for the return.

There will not be time to stop and smell the roses. There is no shortcut through to departures, so you have to exit from arrivals, walk down to security, and enter. I would pick to sit close to the exit, so you don't leave the plane last. As they will start boarding quite shortly after the last passenger leaves the plane.