Gervais is making a category error. ''God' isn't a naturalistic claim. It's not subject to scientific evidence. It would need a specific definition of evidence for or against which would need a methodology to evaluate the claim. In the absence of such a methodology, which you have been asked for many many times, and failed to provide, thr claim has no logical coherence because it is not subject to evidence.
You are proposing then that logic only operates within naturalism. You would need to make the case for that.
What you are saying is what I think you’ve been alluding to is science is the only methodology possible and so logic does not work without science which doesn’t work without matter/energy.
However, let us take the argument from contingency contingent things depend on something else for there existence. We cannot be left with inexplicable or unreasonable contingency so that gives a space in logic to be filled by a non contingent entity.
There you go then, that looks methodical and logical.
You see Sane, the distinction between the natural and superficial is recent and arbitrary.
Your proposal that God is incoherent and illogical is certainly controversial.
