My younger brother doesn't leave my stepmum alone either. She just ignores him, which ishard for her to do as she is still struggling with PND, and eventually he gets bored of it and goes and watches a dvd.
In your case, I think you would have to try things a bit differently. Try sitting him in his high chair where he can see you but isn't in your way? And give him some snacks or toys to keep him occupied. The issue is that he has to learn that he can't be held ALL the time.
It will take time, but just extend the amount of time it takes you to respond to his tantrums buy 30 seconds or so each time, and praise him if he spends even a minute not screaming.

I hope it helps a bit, it's just what we tried with my little brother and it has mostly worked (he has a few relapses every now and then, but my stepmum can now get dinner cooked.)