I don't think my game is a simple reformulation of quantum immortality.

I don't even believe in quantum immortality. At least it is not implied in any way by MWI.

It is perfectly possible that you have increasing amounts of "quantum luck" in a lot of branches, but finally you die in each of the branches, because the life-supporting miracles increase your life less and less, and when they hit the resolution of time, you simply run out of them and die for sure.

If you think time is continuous, then think of the Zenon paradox to see why the infinite sum of such pieces can add to a finite amount of time gained.