Anyway, I still want to know whether being close to a 'landmark' (like a supermassive black hole) is going to significantly increase one's probability. And whether, if tons of copies of you are made and sent far and wide, you should 'anticipate' waking up close to a landmark.

The theory predicts many artifacts of this form. I don't think that landmarks are too significant, because specifying what "supermassive black hole" means is a little complicated, but for very easily specified landmarks it would be the case.