Robin, if you do leave him out of the cage you will have to bird proof the room he spends that time in, no wires and such but I think you should just leave him out when you are there and when you have to shut him up in his cage provide plenty of foraging opportunities to try to keep him busy.
Maybe he doesn't like his cage, is it big enough, see if there is something about the cage itself that is contributing to the problem? He is awful young to have developed a plucking problem but maybe others will have some advice for you.