Peter, why do you assume that only a sober and ordinary state of mind is the most "accurate" and "lucid" state from which to try and understand reality?
Why do you assume that an altered state of consciousness (whether brought on by meditation, psychedelics, tantra or any other means) is a "spiritual dead end"? Isn't that arrogant? Assuming that you can say definitively that all experiences other than the ones that you personally like, are the "real" way? And that anyone who disagrees with you wasn't "serious enough" or "intellectual enough"?
When you say that your holy trinity is intuition, rationality and life experience (filtered by objectivity) - why do you assume that when it comes to the "big questions" such as "what is reality" or "what is the nature of consciousness", that these answers can be found using objectivity alone?
My experience with spirituality started out when I started investigating the nature of consciousness, as that's the thing I find the most interesting in the world. The more I started to think about what consciousness is, and what qualia are, and the hard problem of consciousness, and then started to think about evolution, and cosmology since the Big Bang. Questions such as "how did something come from nothing", "how did life come from non-life" and "how did consciousness arise from non-consciousness" are fundamental to this investigation. Especially given that as Descartes rightly said, the only thing we know for ABSOLUTE certainty is that we are conscious. Everything else could be an illusion.
In fact, the more we understand about science the more it becomes apparent that what we think of as "reality" is hopelessly biased and limited according to our senses, our brains, and our status as four dimensional beings in a universe containing higher dimensions. For example what we think of as the "present moment" is actually in the past, since it occurred a few milliseconds before our optic nerve translated it to the brain. What we think of as "solid objects" are when we look at them atomically or subatomically, mostly empty space. When we think we touch an object, we actually never really touch it. Our perception of time is continuous, but in reality we are always operating from a handful of short and long-term memories as a mnemonic from moment to moment. And the "self" that we think of as static, and fully human, is made up of more bacterial cells than it is human cells, and both these and our human cells are constantly dying and being replaced, just as our memories are mostly fading away, at any given time.
Likewise the more philosophy we learn, the more it's seen that our understanding of the world is also blinkered by the tools of words that we have to try and understand reality. Whenever we try and understand something for which there is no word yet, we have to try and explain it using existing words. Using metaphors and similes. "Such and such is like such and such". But something is always left out. And reification is likely to occur, where we start to mistake the "word for the thing" itself. We can see this when we look at our understanding of physics, and we imagine "particles" to be circular balls whizzing around, when actually particles don't look like that and are simultaneously waves. But reification is actually seen in most areas of language.
The thing is, objectivity (while very useful) is not the be-all and end-all of knowledge. In fact in the great book The Master and the Emissary, this is explained as a function of our brains. The left brain is mainly responsible for understanding reality by breaking things up into chunks. The right brain is mainly responsible for understanding reality as a whole, synthesised, without division. But because words are a function of the left brain, the right brain often cannot communicate its knowledge in a form that is easily understood "objectively". That's why altered states of consciousness are actually very valuable. In transcendental meditation, as with psychedelics, the left brain dominance is suppressed and there is more communication between the hemispheres.
The other issue with "objectivity" as the only valid metric by which one should evaluate spiritual ideas, is that some spiritual questions are INHERENTLY subjective. The nature of consciousness is something that cannot fully be understood objectively, as the hard problem of consciousness shows. You do not know for absolute certain that anybody else is conscious, apart from you, because they could be what are called "philosophical zombies". The nature of a qualia is something that can only be understood in first person. By the person whose qualia it is.
That's why when you start thinking about "what is the nature of my consciousness" part of the answer must be within your own subjective experience of consciousness. It cannot be logically inferred only from observing brains in MRI machines, or from doing a Turing test.
(That's why most New Age or Buddhist or Hindu teachers will start off by asking "who are you" as the starting point for which to begin your spiritual journey).
The fundamental questions of "what is the nature of reality", "what is the self", "what is consciousness" etc cannot be fully understood in a "clinical and objective way" using logic alone. Although actually logic can still be very useful - I came to realise consciousness was a spectrum by reading Descartes and then a lot of different philosophers and scientists including evolutionary biologists and physicists. The more I logically explored the evolution of life on earth (from single celled organisms and those originating from chains of proteins in primordial soup), things like viruses that seem to straddle the boundaries of what we consider "life" and "non-life", and the evolution of the brain I came to realise that there was no "one point" where suddenly "life" or "consciousness" began. Just like how in the womb, there is no one cell that suddenly divides and a baby becomes alive or conscious. There is no one cell in your brain where if you zapped them one by one, you'd suddenly go from alive to dead. And what we consider "dead" for legal purposes isn't necessarily fully dead either. Everything is a spectrum.
Then the more I explored the nature of my self, and realised that there is no true divide between what my "self" is and what the "environment is", and that everything in the universe couldn't exist the way they do, without the precise positioning of everything else, at any given moment, that's where the logical understanding of nonduality came in.
But logic only gets you so far. Because reification means that you can read the words "everything is connected and everything is consciousness" and even if you logically see how they all fit together, you don't truly understand what it means, behind and beyond the words, unless you're activating your right brain understanding more. Unless you have a mystical experience. That's when you suddenly see that it's true. And you feel it.
That is the core realisation behind many religions. "That art thou". "I AM THAT I AM". That at your core, you are one with everything in existence. And that your consciousness, the awareness beyond words and concepts, the consciousness of a newborn baby, is the same consciousness that expresses itself at different levels of complexity in all of existence. (When I say "consciousness" please do not think in terms of human consciousness, this is an example of how bad words are at trying to express things like this, what our consciousness is like is highly specific to our brain structure, our existence in four dimensions and our sense organs, and involves a language of understanding composed of images, words and mathematics, but when I say consciousness I mean the underlying awareness of subjective experience whether through a brain and nerves or not).
Perhaps you will scoff at everything I say and think it's nothing but "groovy mysticism" and if that's the case, no worries. You keep going down your path and I hope you find your version of enlightenment. I know that Buddhism also does have nonduality at its core although as far as I have learned most Buddhists don't like referring to a self or consciousness, instead using words of negation (not-self) to imply the paucity of words to truly capture these ineffable mysteries.
