Okay, I feel stupid. Before I post a thread, I always do research ahead to be sure I am not wasting people's time. But in this case, my initial research missed the fairly obvious answer.
My original understanding of the webbing orientation is correct, as shown in the "To Tighten the Seat Belt" diagram here:
So I am not crazy, it clearly does cross over differently than modern belts. Those wacky Brits!
Case closed.
So the answer to Stretch's original question is, apparently, yes.