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.