What does it mean, "specified everything exactly"?

This sounds like a slightly modified (at most) version of timeless physics. A function would deterministically assign arrows to each N-dimensional set of coordinates without even looking at its neighborhood, and this function just happens to define an N+2D surface. Points on the surface would still show the relationships we call causality, and by assumption they still exhibit the functional equivalent of our consciousness.

If you mean Many-Worlds does not apply to that reality, well, we don't know for sure that our reality doesn't work by Bohmian mechanics. Maybe we should give this a larger probability. In that case I don't see myself changing my own probability of having subjective experience.