People seem to be saying that they are drawn to Orthodoxy for two main reasons: its claim to historical continuity (thus being the only true church); and its æsthetic attractions. Their third reason seems to be the opposite, not why Orthodoxy
drew them, but why Evangelicalism
repulsed them: which is not in the least surprising in view of its weird mutations you often refer to (which can be observed here in Britain too, though
perhaps to a lesser extent as yet).
What I don't seem to have read in the above posts - unless I missed it, for some are very long - is the way Orthodoxy allows more mystery concerning God and religion, whereas Evangelicalism seems to claim to have all the 'cut-and-dried' answers; though I suppose this could be included in the third reason in my first paragraph. The place and presence of mystery - is the correct word the
apophatic approach to God? - is attractive, after one has moved for decades among brash, self-assured Christians who know all the answers.
(Not, of course, that one can't give space for mystery and still remain a Baptist!

)
I think there is quite a bit of truth to this. In fact, much of what you say is what has drawn me towards Orthodoxy.
However, what has also done it is - ironically enough - my pursuit of philosophy and logic. For a while I was at odds with many of my Baptist friends (I was and am an odd Baptist) because I would reason through some of our beliefs and go, "Well this isn't right." Then by looking at Scripture and examining the ancient Church, I deducted that we should believe
x. I did this with a number of beliefs and for a while pondered whether or not I was just a heretic lacking the power of the Spirit.
Then I began working at a place where the owners and vast majority of the office staff were Orthodox. One of them graduated from Holy Cross in fact. So he and I began having multiple discussions about Orthodox theology, because I was interested to learn something new. What struck me is that every belief I reasoned to was already believed in the Orthodox Church (or I was at least close to it, enough that it was hard to tell a difference). Now certainly there were and are some extras that I disagreed with or had not considered, but for the most part much what I thought a Church should believe was already believed by the Orthodox Church.
To me, I read that as being nothing special in me, but instead the Holy Spirit guiding me along a path, one I'm still on. So the main draw to Orthodoxy isn't that I'm a disgruntled Protestant (though I am that in some ways...part of the reason I haven't converted to Orthodoxy is my fear that it may be out of bitterness), but instead that I fell in love with the teachings and way of life before I new there was a beautiful structure in place that already held them.
But one of the conclusions I have is that if Orthodoxy holds Truth within, then it holds Hope as well, for the two are one in the same.