Bwahahaha!!! Its OK, I can laugh, I’m not a Brummie. I merely live here - I’m a Lancashire lass at heart. 
You’re not kidding … when I left Suffolk I lived in Norwich for a while. I needed a translator. 
It is definately pronouced Store. I attended Holbrook High School and one of our form names was Stour pronounced “Store”. It has been pronounced this way by many generations of school children. When I was growing up on the Shotley peninsular I only ever heard it being refered to as the “Store”. I think that Stour is a harsher and less attractive word for the beautiful river that it is. So by that rational alone I think that the record should be set straight once and for all. Stour = Store not Stower.
I think it’s pronounced “zombie thread” but I may be mistaken.
I look down on you all. I’m from Kenilworth, which is like Coventry (the city in Shakespeare country 
) but for posh people.
And we have a castle.