but relying on human intuitions to understand the ontological nature of something transcendent

This is way deeper than the Tzortzis debate. We certainly cannot rely on our intuitions, but we ar bounded to our nature. As far as we can tell, we are animals molded by an evolutionary process that happened entirely in a tiny part of the history of a single planet. Both our intuition and our intellect should be limited by this.
When people search for transcendence inside of their own minds they are making a very presumptuous claim. They are claiming that their own self contains something that transcendent. It is funny to call such a thing transcendent though.
Science, on the other hand, is our means of transcendence. It makes our understanding surpass our most naive instincts and allow us to expand our knowledge to the edge of our capabilities. This is as far as transcendence can go.