Wow, I never knew who wrote those Paramount stings. How did you find that out?
As I recall, the original home video release wasn't fully in black-and-white; it was intercut between color footage from "The Menagerie" and black-and-white footage from Roddenberry's surviving copy of "The Cage." If it came out in '85, it stands to reason it would've had the Schifrin sting and the blue logo.
(CLG Wiki's Paramount Television logo description page)
Of course, we already know Schifrin was the genius behind the Mission: Impossible
title theme music.