That's the problem isn't it, what exactly is the measure for an "Immortal"? Premierships, SOO, Kangaroos, coaching, or as the NRL vaguely puts it "to have changed the game or had an impact beyond his career". Who else qualifies?
I don't think most of those that you listed "changed the game/had an external impact", Thurston, like Beetson, almost definitely meets the criteria. McCarthy certainly changed the way 2nd rowers play the game, even up to today. Think of all the good 2nd rowers and they are all basically McCarthy clones (from Clyde to Kikau). I think Mortimer qualifies on a number of grounds, take 1, cover defending, traditionally a lock's role, Raper set that mold, until Mortimer came along. I think we can safely put down at least 2 premierships to his cover defence. Take 2, the legendary kick and chase, no one perfected it like Mortimer. In comparison Sterling was "cookie cutter" half back, nothing "new" in his game.
Talking about teams, St George have 5 with 4 of those from the same era, when they had the money to have an almost professional team playing against other teams that were mostly all amateurs/part time footballers. Chooks have 3, Souths 2 and Newcastle, Canbra and Brisbane 1 each. (Yes, I know some of them played for multiple teams but the most games, prime of their career, et).
Look at who had the influence with the NRL and the media, for example St George had Frank Facer, maybe that's the best measure of immortals, who pushed their case the most. In our corner, Peter Moore who was not well liked at RL headquarters and now Gould that's interesting.
Always a Bulldog