how exactly would you distinguish the universe in which we live in from the universe in which human moral change was determined by something like a random walk through value space?

If you use this analogy again in the future, you may want to be more precise.

• Maybe by "random walk" you convey the idea that human moral change is nondeterministic, or depends on conditions in such a way that change in one direction is just as likely as change in another direction;

• Or maybe by "random walk" you mean that human moral change is robust and deterministic, but does not approach any kind of limit, or approaches a limit that is very far from our current position in values-space.