The 3D tilt-in title also feels weirdly out of place.
I stole that. I don't think it's timed quite right, either. Nor, surprisingly, could I find clean generic "swoosh" effects that really sounded anything like TOS.
I wondered about that.
The most sophisticated titles of that era would have been might've been something Robert Able-esque. Certainly nothing 3D. Contemporary shows were not so sophisticated in their titling:
Logan's Run series titles
Fantastic Journey titles
Space: 1999 1st season titles
Also, I seriously doubt the show would ever have hit the air wit the title "Phase II". The marketing people would likely have just opted for "Star Trek 2" or something.