There really IS a "way" you know & you are on it, but at an early stage.
Sorry you doubt my depth (!!). So many of my students have recognized right away that I was 100 proof, 24 carat, the real McCoy!! I was surprised because there is no proof, but it wasn't real surprise because I understand the phenomenon.
If you want to know how someone "feels" toward you ask yourself how you feel about them. Action & reaction, says Sir Isaac Newton, are equal & opposite (& so far this law has held).
Feelings are funny things. So is friendship & love -- defying reason -- and since this matter we are dealing with is akin to both friendship & love ("one thing" anyway) it also defies reason -- but not feeling.
(Granted that one may be wrong once in a while -- but after I have known a person a while then there is no such possibility. For example Brunton, Gurdjieff, Cagliostro, Nostradamus, --- all remarkable me, but I have only met one of them, Brunton, & that only twice, not enough to judge because I was then a seeker, in a highly emotional state, and a student myself. What about D.T. Suzuki, Sri Aurobindo? I met Suzuki twice. I am very suspicious here because they turned out such a big volume of words & theories. Zen Masters do not do that!
Who would I regard as "awakened"? I think Krishnamurti, whom I have met, and the Maharshi, who has a down-to-earth common sense & is reasonably brief & to the point.
(Plus thousands of unknowns!)
Maybe I should say that there is an "intellectual" sort of "awakening" (Zen?) which produces a similar understanding & lasts through life, which lacks SIMULTANEOUS direct contact and ability to experiment with (!!) the Entity which is the One.
"Mystical experience" is unconscious or only partly conscious (& leaves ego untouched!). The need is to have this wonderful but evasive and non-evidential thing SPREAD OUT FOR EXAMINATION IN THE FULLY CONSCIOUS MIND -- the one you use in your sceptical way (& believe me I am far more 'sceptical' than you will ever be -- being a mathematician & ex-public-accountant).
You keep falling over one & the same thing.
You are looking in the South for the North star!
To be specific. You "raise" questions as to life after death, "reincarnation" & so forth. No answer to these has yet been furnished by experiment. That is the only way to get an "answer," if it is possible. (God tantalizes you with "ultimates.") However when you become "awakened" your whole understanding of concepts, the self, time, space, perception, etc. is DRASTICALLY OVERTURNED.
This IN TURN powerfully affects the consideration of your "questions" (obviously an "after-life" for example IMPLIES that "time" goes on just as usual without your mind OR ELSE that mind itself survives -- and I doubt that!)
Thus "questions" are ALL disposed of, as mine have been, and in the following ways:
(a) SOME are recognized as having no meaning in themselves & thus as "no questions."
(b) SOME are answered.
(c) SOME are seen to be incapable of any answer (since they are things to be 'accepted,' like the One).
You are AHEAD OF YOURSELF. For a .04 stamp you wish to peep at the hidden records of the Universe!! Seriously you must first get "awakening" to deal adequately with some of your "questions" -- OTHERWISE THE ANSWERS WOULD HAVE BEEN PUBLISHED LONG AGO IN THE NEWSPAPERS! EVER THINK OF THAT? WORDS CAN BE PRINTED.
I note Brunton says Jesus came from another planet. This sort of "information" rings ALARM BELLS in me at once, -- & involuntarily I say to myself "baloney, how does HE know?"
"Reincarnation" is theosophy. In the East it is "rebirth" & that involves NO REAL CONNECTION with you, only a continuation of "tendencies." The "Perennial Philosophy" contains innumerable quotations from genuinely awakened men. Why "apologetic"? 
[1. R. had referred to Huxley's writing style as "apologetic possibility."]
I still don't know for sure what an existentialist is.  WHAT IS IT? Then I can say if I am one!! Has "awakening" increased my knowledge of "life after death"? Certainly -- but not as this "self."
[2. R. had asked if Pulyan were an existentialist.]