Is there another teacher doing the same year? I would demand he move class.
I've read your letter and I think it gives a little too much. By talking about a bad reputation, you are giving this woman an "out".
I would make a list of specific examples, and include them in the letter, including the Sats incident, the "raping" incident, and everything else you can think of.
I would say in the letter...
"I am becoming increasingly concerned with the fear with which my son is viewing school. It is not an exaggeration to say he is frightened of Mrs W. I do not use this term lightly, but it is my sincerely-held belief that he is being bullied, not only by Mrs W, but also by other children, who are aware that blaming my son for trouble is an easy way of diverting blame from themselves, and as Mrs W is of the opinion that my son is a liar, and as a result it makes no difference how he defends himself, or indeed if he is guilty or not.
"I would ask you to consider the following examples
(list)
"Please understand that if my son were guilty of trouble I would have no problem with school discipline, which I believe is important. However, it must also be fair.
"I would refer you for a character reference to Ms xxx, who had my son for 5 days while the rest of the class was on a school trip, and commented on how polite he was.
"I think the only course of action now is for him to be moved immediately to another class. I also require your immediate reassurance that Mrs W's threat that she will send a negative report to his secondary school is unfounded. My son deserves a fresh start at his new school, and his understandable nerves at going to his next school are not being helped by this threat."