Why is it that the 70mm prints lacked the "II", while the trailers and posters had it? I'm guessing that the change was made late enough that the "II"-less version had already been shipped out to make the 70mm blowups (due to the longer lead time), and it was too late to change it for the 70mm.
I can tell you that the original "no II" 70mm prints of ST II were shipped out internationally after the first few weeks' screenings in the USA. In Australia, we got ST II an agonizing three months
after the US premiere and we definitely had no "II" for the sneak preview, the premiere and the first few weeks of screenings Down Under.
Note that the novelization has no "II".
Sometimes, in the 70s and 80s, film companies were discouraged from shipping the original heavy reels back to the US after the premieres, to save on freight costs for surplus reels that would be destroyed anyway. That's why many "lost" films end up in countries other than their place of origin.