Hunting air rifles are quite effective. Any .22 Cal or larger at a minimum of 1000 fps will make short work of raccoons. Just treat like a real firearm for safety. And the practice is loads of fun.
Ok, I read too fast the first time. They carry prey to where they feel safe. Up a tree puts them above other predators. Secure and free range are hard to put together. I don't know any way other than to supervise. And the surest way to get rid of a predator is to eliminate.
Probably too early in the day for a GHO, but they do begin to get active at dusk so not impossible. It also could be raccoon. Was the fur found with the duck?