Could someone actually be one of the master classes, or are they reserved for people who complete a dead session? Because a master class in the normal game, I feel, would really mess up the balance of power or whatever because of how strong they are.

We only know they only happen under special circumstances, but we don’t really know what triggers them. Yaldabaoth seems to just pop up in random 4-Player Sessions no problem so I can’t see why a Lord or Muse couldn’t be in a normal Session because of something specific.