Great work tallying up the scores! I just take them as they are ;).
But yes, the problem is that the winning strategy here is simply to jump from one hospice case to another. I basically submitted a team with about 10 bad picks, because I knew that as long as I can replace the good picks with other good picks, I can score well. Now, such a game might be a good idea, because it's something we don't really have yet. But I think it is not what you wanted it to be? In this case, I would suggest closing it down. An opportunistic pool wouldn''t even need a beginners' pool of 20. Maybe only 10. Once you are above 10 you run out of "good" names, and you end up with people like, say, Pelé, who might take their time.
Introducing some kind of queue might be interesting though. Then the game becomes some kind of "mid-distance run". We don't have a lot of games like that, maybe only the Poker Pool with it's 7 months.