I recently heard a radio journalist saying that someone had \e‑'shüd\ (Merriam-Webster transcription) something. Certain that the journalist had mispronounced it, I looked eschew up in Merriam-Webster's eleventh, and to my surprise the pronunciation was listed as \e‑'shü, i‑; es‑'chü, is‑; also e‑'skyü\. According to the dictionary's frontmatter (p. 12a), only the one following also is considered a variant pronunciation, and we are to draw no conclusions on the comparative popularities of the pronunciations that precede it. But still! I mean! But still, I mean I'd never even heard \e-'shü\ before, which may mean only that I need to get a life. (The previous sentence strongly suggests that I do in fact need to get a life. A normal person--one who's not in the editing biz--would have put "only" [or "just"] before "mean," not after it. Pitiful.)
(Or maybe "only mean" would have been correct as well as idiomatic. I mean, the fact that I'd never heard \e‑'shü\ before only means I need to get a life; it doesn't build pyramids. On the other hand, I may only need to get a new line of work.)
But seriously now, the reason I'm bringing this up. I looked up eschew because I thought I'd heard it mispronounced. The first pronunciation listed (the first among equals) was \e‑'shü\; but--and here comes my point at last--the syllabification is given as es·chew. This makes no sense if the sch is pronounced \sh\, but it's the only break that makes sense if the sch is pronounced \s‑ch\. [An apologetic retraction for the rest of this paragraph appears here. June 26, 2008.] So Merriam-Webster is contradicting itself. It doesn't take a stand on the pronunciation of the sch, but it does take a stand on the syllabification, which means that it does take a stand on the pronunciation of the sch.
The Oxford English Dictionary takes a different approach to syllabification. In an entry where no pronunciation guide is given, accents appear at the beginning of the stressed syllables in the main entry. If a pronunciation is given, the accents appear in the pronunciation, and the main entry has no syllabification. Thus, the OED has "antidisestablishmen'tarianism with no pronunciation given.* Slicing it down little by little, we find dise'stablishment and finally establishment, with the pronunciation given as (ɪ'stæblɪʃmənt). The main entry lacks an accent mark since one appears in the pronunciation. (The OED uses accent marks at the base line for secondary stress. Since I don't know how to get those, I use double nonsmart quotes for the secondary accent.)
I propose that we stop worrying about syllabification. If a break is plausible and gives syllables that can be pronounced and isn't absurd, it's fine. I realize that this attitude is similar to that of the author who says "Since I don't understand dangling modifiers, they aren't important." This author is only partially correct. Dangling modifiers aren't important (except, God bless them, as part of a full-employment program for manuscript editors). But the author's not understanding them isn't why they're not important. But I'm digressing again. The point is that I realize that my attitude toward syllable breaks is willfully ignorant, but I'm still right. Merriam-Webster and the OED should adopt the practice of putting an accent mark before the stressed vowel, not before what they suppose to be the beginning of the stressed syllable.
None of which tells us how to break eschew.
* I looked antidisestablishmentarianism up in the OED because it presents many an opportunity for syllable breaks. The OED defines it thus:
Properly, opposition to the disestablishment of the Church of England (rare): but popularly cited as an example of a long word. So antidisestablishmentarian.