I'm partial to the shift key+z typo answer.
If you're typing OMG really fast (cause you're so excited) you're going to slip and hit zOMG, since the < key isn't between shift and Z on most US keyboards.
Outside of any of the other possible origins, the typo is the most likely because it's most easily 'discovered' by small groups of people who are instant messaging each other. Most likely it has risen out of a parallell evolution because of our natural tendencies (as opposed to being invented or "first coined" by anyone).
Essentially, we all invent it ourselves.
Like J.R., I don't see a good match between the language of the quoted sentence and any clear, recognized definition of churning.
The only definition of "churning away" that I'm familiar with carries a sense of purposeless activity; essentially it means "churning without a definite goal or foreseeable end," as in "He left the refrigerator door open, and the motor was just churning away all afternoon."
"Churning away" emphatically does not mean churning productively—not even at the impersonal, quota-driven level of "churning out," which, as Merriam-Webster's Eleventh Collegiate notes, involves "produc[ing] mechanically or copiously," but which frequently harbors an implication of poor or indifferent quality in the resulting output.
Making sense of the author's description of women churning away "dreams, fears, social [intrigues] and political intrigues" is complicated by the fact that one of the churned-away things (dreams) seems desirable, a second (fears) seems undesirable, and a third (intrigues) may be desirable or undesirable. Under the circumstances, it's hard to tell whether the women intend the churning to produce these things—or indeed whether the women have any clear intention at all with regard to their churning.
Maybe the author chose "churning away" to avoid the unflattering implications of "churning out." If so, I think it was a bad decision, since "churning away" does an exceedingly poor job of conveying what (I suspect) the author means. I would have suggested ending the sentence as follows:
...where the women of the home give voice to dreams and fears, and where elaborate social and political intrigues play out."
An author determined to tie the sentence to a kitchen-friendly verb could have used "cook up" or "brew up." Both have weaknesses of their own—"cook up" suggests fabrication of a deceptive kind, and "brew up" has witchy connotations—but at least they aren't borderline nonsensical, as "churn away" is.
Best Answer
I found a use of the phrase that predates the Maggie reference by a decade in an 1884 student publication of the University of Michigan called The Chronicle. It occurs at the end of a short story about a man courting a woman who says she cannot marry him but won't tell him why. Finally she tells him it is because she has cold feet. It is italicized in the original as if some sort of punch line to a joke:
I also found the story of the German card player, or at least a version of it. This is from An Old Story of My Farming Days: (Ut Mine Stromtid), by Fritz Reuter, (translation date 1878):
Interestingly, there is another reference to cold feet in another book by Fritz Reuter called Seed-time and Harvest, also 1878, as some sort of joke involving a shoemaker:
Unfortunately, none of these references shed much light on why the phrase came to mean what it did. At least not for me. I thought the references were important enough to include here, though, and maybe someone else (a German speaker?) can take the pieces and complete the puzzle.
Edit, 6/28/11:
After doing a little more work on trying to figure out the intended humor of The Chronicle story quoted above, I came up with something that may shed more light on the phrase.
What I found was this reference in an issue of the Otago Daily Times from 1881:
After a little more sleuthing, I found that this maxim was quite common among Presbyterians, at least, in the 1880s. The idea being that missionary zeal needed to be paired with a concern for meeting the social needs of those to be converted. Apparently the original phrase went something along the lines of "Man cannot be converted while suffering from cold feet or an empty stomach." I've seen the phrase attributed to a half dozen different ministers in the early 1800s—it seems no one knew for sure who first said it. The important part is that the saying was commonly known in certain circles. Given that, and given that the University of Michigan was co-founded by a Presbyterian minister and probably still heavily populated by Presbyterians in 1884, I think the joke of the The Chronicle story may be a play on this religious maxim. In other words, since Evelyn has cold feet, she cannot be "converted" to the idea of marrying Ernest.
If this is the case (and I realize it could be a big "if") then I think there may also be the possibility that our modern idea of having cold feet could have been influenced by this same phrase. That is, as a corollary to not being interested in being "saved" when one's feet are cold, one's having "cold feet" may have come to mean one's reluctance to pursue a matter—perhaps popularized with jokes like the story above.