Can you provide a compelling argument that would convince a rational individual to take sastra (scripture) literally in its entirety, as opposed to metaphorically, figuratively, poetically, etc.?

I am not sure that one can accept sastra in its entirety simply by arguments. There must be realization. When we read the Gita or Bhagavatam and experience its reality by higher consciousness, then we accept it.

There is no way to convince a child of advanced physics, because the child can not understand it. So one needs some spiritual qualification to enter into the sublime mystery of sastra. By argument, we can convince reasonable people to be open-minded and explore Krishna consciousness.