The mere existence of what seem to be valid questions that pierce the limits of science, is itself evidence against the science only view. A fundamental separation of nature and the supernatural seems in order to me.
That which is beyond the limits of science is uncertainty, that is things that cannot be understood more clearly by the use of objective experimentation - it is spurious to use this as a basis for a dichotomy between the natural and supernatural. There is no evidence in support of the supernatural.