In the first branch, you are assuming the existence of uncountably continuous time and space with perfect precision. Scientific observation is not on your side. (Plancks constant, QM, for example)
For the second, if the universe were somehow rational, there is no need to drag in irrational numbers to describe it.
I don't believe I'm assuming anything. I asked specific questions. The answers to those questions are relevant to what the OP wrote. Your last sentence does not make sense to me. The universe is not a number and therefore is not a rational number. It is not rational in the sense of thought either since it does not think (as far as I can tell). I have not idea what is meant by the statement, "if the universe were somehow rational...".
For the second, if the universe were somehow rational, there is no need to drag in irrational numbers to describe it.