I once read somewhere that when a parrot is doing behaviour such as this, he could get overstimulated by his new found freedom, and lashout with emotion in figuring out this new ability to control his environment in his being able to fly. The advice I read was that is is important for YOU to be in control, and that meant when he is on you and being good, that you make the first move and have him step up and put him elsewhere, perhaps on a tree stand or perch even if hes only been with you a couple of minutes or so, then praise him for how good he was. Don't allow him to stay long enough to do damage to you. Leave him wanting more.
I'm not sure if I understand correctly, but are all your play stands and perches eye level? Most birds prefer to be up high so I wouldbe sure to place them up as high as possible, it gives them a secure feeling.