I was in a pet store today that carries parrots. A lady who has a grey came in and the owner was there so I asked them about screaming.
Both said it was uncommon for greys.
Apparently I was just lucky in knowing the couple of screamers that I've had contact with.
They are excellent talkers and mimickers.
So, based on those with far more experience than I, I was wrong.
Consider the grey.
Greys will scream if not redirected towards talking, or when around other birds that don't talk. Screaming is basically an attention getting behavior. Your results on that are more about the time you have to work with your bird... or so I find it to be.