That is, a million identical starting points like our world would need to end up after that billion years within a very small volume of morality-space, in order for this process to be meaningful.

(The hypothetical I posited doesn't start with our world, but with an artificial isolated/abstract "research project" whose only goal is to answer that one question.) In any case, determinism is not particularly important as long as the expected quality across the various possible outcomes is high. For example, for a goal of producing a good movie to be meaningful, it is not necessary to demand that only very similar movies can be produced.

Considering that the 4 billion years (or so) spent by evolution

Evolution is irrelevant, not analogous to intelligent minds purposefully designing things.

presumably another billion years of evolution would have to be considered as a "nothing going wrong" method

No, see "value drift", fragility of value.