Thank you for your detailed, thorough reply. It deserves a thorough response in return, but I must respectfully leave that to someone else, as my interest in Wittgenstein is not nearly enough to sustain such an effort. So I'll confine myself to commenting on just a few of your points:
First, if Wittgenstein was a logician, then I have to ask what his contribution to logic was. As far as I can tell, he never made one... certainly nothing even approaching Godel, who actually revolutionized logic. Wittgensteins impact on logic, on the other hand, was on all accounts nonexistant.
Maybe Wittgenstein was, as you say, an anti-logician and a philosopher. I won't dispute that.
You write:
"I see nothing mystical in these portions of the Tractatus, and I think it is a bit of a leap to call him a mystic on the grounds that he technically did not reject mystical/ethical statements as being false, only nonsensical and thus on par with tautologies of any kind."
How about these parts of the Tractatus:
5.621 The world and life are one.
5.63 I am my world. (The microcosm.)
6.432 How things are in the world is a matter of complete indifference for
what is higher. God does not reveal himself in the world.
6.44 It is not how things are in the world that is mystical, but that it
exists.
6.45 To view the world sub specie aeterni is to view it as a whole--a
limited whole. Feeling the world as a limited whole--it is this that is
mystical.
6.522 There are, indeed, things that cannot be put into words. They make
themselves manifest. They are what is mystical.
6.54 My propositions are elucidatory in this way: he who understands me
finally recognizes them as senseless, when he has climbed out through them,
on them, over them. (He must so to speak throw away the ladder, after he
has climbed up on it.) He must transcend these propositions, and then he
will see the world aright.
7 What we cannot speak about we must pass over in silence.
These are the statements that W chose to culminate his
Tractatus with. They are what the rest led up to (6.432 combined with 6.522 and 7 are especially telling -- to take just 7 and use it in an anti-religious, anti-mystical way as the Logical Positivists did is a perversion of Wittgenstein's obvious intent here), and they are both explicitly and implicitly mystical.
Explicitly because he talks about mysticism itself. He addresses what is mystical, he defines it, it (and the transcendent) is what he at the crowning point of his book concerns himself with.
They are also implicitly mystical because the language and process he advocates are in the mystical tradition. The mystics often talk about the transcendent reality and God as something that can not be spoken of because it transcends human conception, words, and naming, and rather approach it apophatically (as that which it is not). So too does W approach what is of greatest concern to him.
The metaphor of using what one says as a ladder to climb up to the transcendent, at which point the ladder is no longer of use, is another common mystical metaphor. As the transcendent or God is beyond words, then what one says can only at best be a means to get there, and is not itself the point at all.
At the very least, I think you could say that W appropriated mystical and religious language to talk about his philosophical concerns, but I think there is more evidence (apart from the already cited sections of the Tractatus) that his concerns are actually primarily religious rather than philosophical. W himself said that "I cannot help seeing every problem from a religious point of view", that "Bach wrote on the title page of his Orgelbüchlein, ‘To the glory of the most high God, and that my neighbour may be benefited thereby.’ That is what I would have liked to say about my work." W's close friend Norman Malcolm wrote "Wittgenstein’s mature life was strongly marked by religious thought and feeling. I am inclined to think that he was more deeply religious than are many people who correctly regard themselves as religious believers."
The last thing I want to address is your question (in regards to the statements in the Tractatus) "in what sense do they not follow?"
In a logical derivation, propositions follow one another based on axioms and using the rules of logic (like modus ponens, modus tollens, double negation, etc). Though there do seem to be some sort of axioms and maybe propositions in the Tractatus, they do not follow one another using the rules of logic. There is no such explicit connection between them. It is in that sense that they do not follow.