Forgive me if I am being obtuse, but how do you see any manner of Christian thought, esoteric or otherwise, as a portal through which to achieve that goal? Is the idealism of esoteric Christianity so different from the idealism of the "mainstream" variety?         

The "mainstream" variety doesn't have an esoteric core anymore (Cf. The Destruction of the Christian Tradition). When the kernel was lost, only the shell remained, and that shell is modern, "mainstream" Christianity. We simply assume that people like Thomas Aquinas and Meister Eckhart wrote and taught in a time in which the kernel was "still in place". This kernel, ASBO calls "transcendental idealism" ...

Standard moron:

I don't need religion.
God? Can't prove it. Only what can be proven is real.
Kafka's so good, I read him over and over again.
Democracy is stupid, but it works somehow, you know?

Standard metalhead:
The above +
The world around me is ugly, so Iet's drink lots of beer and bang our heads to loud, ugly music.

I'm tired of it. Everybody, even the lowest low-life, can criticize. Every asshole has an opinion. Do we need to consider them all? No.
Most people are better off working with their mouths shut. Most metalheads too.

Moron: "Did you hear of this new philosopher? Haven't read a better criticism of our media."
Non-moron: "I've read that the world we live in degenerates according to cyclic laws, and that at the start of the new cycle the world will be restored, albeit maybe without mankind."
Moron: "Huh? What's this crazy shit? Didn't you know technology freed man? With it, we're gonna reach the stars!"
Etc.

This is my opinion, of course, and you're free to correct me, but mind the above when you do.

Science doesn't deny that principles aren't demonstrable. By definition, it is impossible to demonstrate an abstraction. What is demonstrated is the actual from which we make abstractions and form principles using faculties of reason (i.e., the intellect -- Aristotle's nous). In science, this is the formation and testing of hypotheses.

How is this not scientific?

First, we should differentiate science in the sense Aristotle uses it and "modern science".
Second, you have described the process "upside down": principles aren't formed; they "are" already there. Reason is logos, nous is the intellect (indian manas). I think 'mind' once had a similar denotation.

But let me quote some of Aristotle, also (NE):
VI, 3:

Again, every science is thought to be capable of being taught, and its object of being learned. And all teaching starts from what is already known, as we maintain in the Analytics also; for it proceeds sometimes through induction and sometimes by syllogism. Now induction is the starting-point which knowledge even of the universal presupposes, while syllogism proceeds from universals. There are therefore starting-points from which syllogism proceeds, which are not reached by syllogism; it is therefore by induction that they are acquired. Scientific knowledge is, then, a state of capacity to demonstrate, and has the other limiting characteristics which we specify in the Analytics, for it is when a man believes in a certain way and the starting-points are known to him that he has scientific knowledge, since if they are not better known to him than the conclusion, he will have his knowledge only incidentally.

VI, 6:

This being so, the first principle from which what is scientifically known follows cannot be an object of scientific knowledge, of art, or of practical wisdom ... the remaining alternative is that it is intuitive reason (=nous) that grasps the first principles.

http://classics.mit.edu/Aristotle/nicomachaen.6.vi.html (I'm not very content with that translation, but it gets the idea across.)

The more I listen to classical music, the plainer the following forms in my opinion:

Herbert von Karajan was a pop star of classical music conductors; he was big on image, but the image was better than what was behind. He was a showman, and that influenced his work. He did not have an inherent desire for quality. The result are some average recordings, and lots of crap that was made chiefly for money or because it suited his egomania.

Karl Böhm was the inverse of the above: less image, more quality music. He realized that his real image would depend on his work, and not on other aspects of his life. Thus, whenever a choice is possible, I prefer the conductor Karl Böhm to the conductor Herbert von Karajan.