I have a friend who used "baby sign language" -- I don't honestly know the name of the book, sorry. When she talked to her child, she also signed, and the child learned to sign some of the words she couldn't form yet, and being able to communicate helped to stop the frustration and screaming.
The other thing you can do, is simply walk away. You have to be sure your child is safe in the high chair when you do it, so she won't try to get out and fall, but the old stand-by method is to simply walk away until the child is quiet, and then see what you can do.
I understand about the screaming. My first child could set me off, too. I don't know whether it was just the two of us together, or whether it was that I was young and wanted to be able to fix anything and everything, and it frustrated ME and set ME off into my own inner tantrum if I couldn't ? Whatever . . . with my 3rd child, I used to hold her and bounce her until she fell asleep, so she didn't cry herself to sleep in the crib. She did often cry herself to sleep in my arms, and I would just sing to her. Any song I could think of, cuz it was SO much better than yelling back. If regular songs didn't work, I tried hymns -- I figured they were very therapeutic. hee hee (Funny parrt of that is that my 8 yr old would be in bed in the next room at the time, and when I'd stop because I thought the little one was asleep, the 8 yr old would pipe up, "Keep singing, Mommy". So I sang more than one to sleep without knowing it!)
I think I'd really give the sign language thing a try. From simply things like, "Do you want to get down?", "Do you want a drink?", etc. As she learns to sign the word for down and drink, you may find that she figures out she can get what she wants, even if she knows the words and can't quite form them.
Good luck ! This is the hardest thing about parenting. It is SO hard to stay calm cool and collected when your emotions are tearing you apart inside. The key is to unlock the frustration inside her, and then the dramatics will begin to subside, because she'll be able to communicate more appropriately and get the response she's looking for, or at least get a better level of communication going.