I call 100% complete BS on your Private Stock story. First the Santana is close to an SG shape but with the top horn slightly longer. If it was a right handed body with longer horn sanded down a bit then it would still be longer or equal to the bottom horn length. 2nd Paul signs every PS personally and there is no way he let what you described out of his building much less with his signature on it. I have met Paul three times and he’s super cool, loves guitars and takes massive pride in his work. Unless you produce a pic of said Santana I don’t believe your claim for a second. If this was 10 top or wood library maybe but doubtful, but a PS each signed by Paul and hand inspected before signing, no way it came out like you say.
It probably looked just like this one as far as the shape goes