The concern that appeals to mystery might be the reprehensible dodge of a cult is legitimate, but in the case of Buddhism misplaced, since there is a rigorous and well-defined methodology for achieving the states described. Buddhism is very non-proselytizing. You can adopt the methods and see for yourself, or not. Take, say, quantum mechanics. A Newtonian physicist being introduced to the concepts would ridicule them as contradictory and absurd. But the quantum physicist would have to appeal to patience and say something like, “once you’ve understood all the maths and the experimental results, your objections will be answered.” In other words, do the work, reconfigure your mind to understand the matter properly. The Zen master uses koans to push the student back into the “laboratory” to achieve understanding. She does not rely on an argument from authority like trust in the pope or the Bible.
I say this as someone who considers themself a kind of neo-Buddhist, in that a lot of my personal philosophy has resonances with Buddhism— and I did study Mahayana Buddhism years ago, though I don’t think this had anything to do with my current relationalist perspective. But I’m not a Buddhist in any conventional sense and I honestly don’t know if enlightenment is a “thing”. However the above is how I would defend Buddhism against the charge of incoherence you make.
It’s a mistake to think you can fully critique Buddhism by tackling the verbal explications of the dharma in terms of pre-existing concepts. It’s not meant to be read purely intellectually as a philosophy in the Western sense. It’s tied to practice and can’t be severed from that.