I thoroughly enjoyed this work and the argument you make is flawless. I agree that the created "nature" cannot empirically examine the supernatural creator, it is beyond the reach of nature. I believe in the Bible and that it is the Word of God (our supernatural Creator.) This allows us to examine the supernatural God experientially, through an examination of His Word. Paul put this notion in beautiful terms in Romans 8 vss. 5-7.
Vs 5 For those who are in accord with the flesh set their minds on the things of the flesh, but those in accord with the spirit on the things of the spirit. 6 For the minding of the flesh means death, but the minding of the spirit means life and peace; 7 because the minding of the flesh means enmity with God, for it is not under subjection to the law of God, nor, in fact, can it be.
The apostle clearly identifies the immutable fact that the "flesh" (nature) cannot examine the "spirit" (supernature in your parlance.)
Since we are created in "the image of God" Genesis ch1 vss. 26&27 we have a spiritual nature that allows us to have a relationship with God. This too cannot be empirically examined, only experienced. It is a sad fact that many scientists are, in reality, fleshly men in the sense that Paul meant in Romans, a consequence of this thinking is that they have cut themselves off from the spirit. This is not an irreversible condition but it requires the fleshly thinker must open himself to it's influence.
Thank you for sharing