You continue to miss the point. In this specific context, volume ratio scales super-exponentially with dimension, and unless you're willing to have accuracy als

You continue to miss the point. In this specific context, volume ratio scales super-exponentially with dimension, and unless you're willing to have accuracy also drop super-exponentially (as in, go very very quickly to zero), then you are wasting your time by trying to perform rejection sampling in a context where you are statistically never going to hit the target set.