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Sometimes it helps to actually click on the articles on google, and see what they cited. A two minute search turned up:
http://psychclassics.yorku.ca/Munster/Industrial/chap17.htm
http://www.worklessparty.org/timework/chapman.htm
http://www.igda.org/why-crunch-modes-doesnt-work-six-lessons
http://hbswk.hbs.edu/archive/5190.html
http://isme.tamu.edu/JSCOPE97/Belenky97/Belenky97.htm

I'm sure a more thorough search would turn up that much more. There's certainly something on JSTOR, for example.

There are studies going all the way back to the early days of mass production to demonstrate that 8 hours a day, 40 hours a week, with regular breaks, is just about the maximum amount of productive time you can get out of anyone on a regular basis. Henry Ford put all his employees on 8-hour days, five days a week not because he was a nice guy, or even because he thought they would make good use of the time off, but because they were more productive that way.

Does not that $10,000 (Canadian) offer assume that your original argument and its rebuttal are worthy of being "accepted for publication in one of the 30 top-ranked economics journals". More so, you place yourself as the judge. Let us also consider what you require:

1. My argument is that the authenticity of the lump-of-labor fallacy claim, with regard to unemployment and the hours of work, is questionable;

2. that various explanations of it are inconsistent and contradictory

3. and that Sydney J. Chapman’s neglected theory of the hours of labor presents a more coherent analysis of the reduction of working time than the often-cited fallacy claim

Before digging into that, let us consider more qualifications on what the hell your point is:

"To qualify for the $10,000 prize, the candidate would need to write an article refuting the main conclusions of my September 2007 article and have it accepted for publication, as a peer-reviewed article, in one of the 30 top-ranked economics journals."

Some poster: "Could you please give a link to your original post, I'd be interested to read it."

Your reply: "The original MaxSpeak post is not available. But I crossposted it on the Work Less Institute of Technology:

http://worklessparty.org/wlitblog/archives/2004_10.html"

Which is a series of unrelated posts. Maybe yours is in there. Do you seriously expect a top 30 economical journal to care about a refutation to some unpublished, unlinked, debloggified post of yours? Do your "top 30" publications all accept "anonymously peer-reviewed articles" which you require? And is that SOP? Forgive me as I am outside of acadamia. Is that anonymous or pseudo-anonymous or is the review board selected from a known group of peers (so you know the set of peers but not the subset judging this hypothetical article). If by chance my article was published but not "anonymously peer-reviewed" then I would not be able to have republished. So can I, as an unpublised submitter with engineering (not economics) degrees, demand a style of review?

Let us consider some of more problems:

a) Damn near everything is "questionable" (point 1 above). You win.
b) Various explanations of anything are inconsistent and contradictory. Thus the use of the word "various" (point 2 above). You win.
c) I stop carrying about point 3, but that is where the heart of any discussion would be. Proving one theory superior to another.

To sum it up, two of your three points are pointless and unrefutable. You are seeking a published article the merits of which you judge that cannot repeat prior refutations ("won't count if the article simply re-asserts the fallacy claim and follows that by grinding out yet another 'empirical analysis'") of some post of yours that the internet seems to have lost.

What have I missed?

Let's start with the disclaimers: I doubt the best solution is 100% government or free market and 0% of opposite. I do lean more towards free market though.

What you wrote is wrong. Let's look at the US (and all industrialized nations) in the mid to late 19th and early 20th century. For starters, they were industrialized because of the free market. Because the free market brought in the industrial revolution most people finally had more prospects than farming. Not that there is anything wrong with being a farmer, it's just that if that's not what you wanted to do in life, before the industrial revolution, you didn't really have many other options.

Those 12 hour days and 6-7 day work weeks were on the way out by the time the government got involved. Labor Unions had done a lot to change that. But even without labor unions, you eventually get people who wise up and realize that a happy workforce with low turnover is a more productive work force. In fact, it is not the government that decided that 40 hour work weeks should be the norm, it was the free market in the form of Henry Ford.

And as for your illiteracy stats, it was the industrial revolution that brought prices of paper down enough which allowed for people to learn to read and write. Also, you're stats are bunk. Illiteracy rates in 1870 was about 20% and that declines to less than 8% by 1910.

I agree, third parties have a lot of big ideas but fall short on the actual work of getting things done. The best example being the work less party. Perhaps a fine idea, but hampered by a lack of work ethic. :-p

Unfortunately, paying people to buy your products doesn't work and never has.

I guess you never heard of Henry Ford ?

"The people who consume the bulk of goods are the people who make them. That is a fact we must never forget -- that is the secret of our prosperity."

Henry Ford, 1926