I do let them out but one pen at a time. I have them separated by breed and I want to keep them pure and the males usually want to kill each other. Years ago I did have a fox and a coyote kill some birds during the day. We are rural and lots of predators...and different that the OP's situation as theirs free range daily.
Your birds are mostly confined after moving them, helps to 'home' them I would imagine.