I don't mean to insult you, but being deaf does not make you any more of an expert on ASL than being hearing makes me an expert at English.
There are properties that specify the term "language" and signed English simply does not have those properties.
From Damned for Their Difference: The Cultural Construction of Deaf People as Disabled published by Gallaudet University Press (2002):
>Signed English, too, is not a language of communication but is confined to contrived situations like the classroom. It is not used within Deaf communities and, thus, has none of the natural dynamics of a natural language, being designed and imposed from the outside.
It seems to me that your error is in linking Pidgin and signed English together as if they are the same. They are not. In signed English, the sentence "The red dog chased the very large cat" would consist of signing every individual word exactly. You would sign "the", "red", "dog", "chased", "the", "very", "large", "cat". Pidgin is a mixture of English and ASL, and you would sign "red", "dog", "chase", "large", "cat". A case can be made that Pidgin is a language, but signed English is definitively not a language.
Signed,
4.0 GPA on 14 credit hours of ASL and Deaf Culture.