"A few thoughts -
1. I agree with you that employment isn't always going to be smooth, particularly when layoffs are necessary, but just because you have a mass layoff doesn't mean it's smooth relative to the relevant counterfactual. In a particularly harsh inventory cycle, all workers may be ZMP. You will see a mass layoff, but you may not see a layoff of all workers - which implies relative persistence despite a large shock. I don't think your post necessarily disagrees with this, but I just wanted to make that point in Leamer's favor. Which leads me to -
2. This persistence story seems to mesh well with the idea of "labor as investment", but that also seems to cause problems for the ZMP story. A lot of the time when Cowen talks about ZMP it sounds like he's talking about short-term ZMP, like the ZMP that might emerge from a rough inventory cycle. But would firms really care about this? If labor is an investment, then what they're really thinking of is the NPV of ZMP, in which case there would be considerably less ZMP as a response to a business cycle (you'd only really expect to see it in cases of technological obsolescence). In other words - "labor as investment" (1.) confirms the idea of persistence, and (2.) makes ZMP more of a secular concern than a cyclical one.
3. Its true I'm young and unread, but I'm a little confused on how this hurts the New Keynesian story. New Keynesians seem to hang a lot on sticky prices and rigidity - far more than earlier Keynesians. This persistence understanding would seem to bolster a lot of those concerns. And "labor as investment" would seem to bolster specific New Keynesian models like efficiency wage models, right? I don't see how this necessarily conflicts with New Keynesianism.
4. I do like how at the end you acknowledge the variety of theories that this jives with. One of my biggest beefs with macroeconomics is that it acts like all these "theories" are at war with each other. In reality, they all describe various processes that are operating to a certain extent. The question isn't "which is right?". They all capture an important element of the economy. The question is "what mix of these processes is influencing the economy right now?""
Tyler Cowen also had a post up recently on protecting employment in a specialized economy. Mario Rizzo and Jonathan Catalan make the obvious critique here and here - if you protect jobs you may be protecting economic dinosaurs. You're going to interupt the innovative process of the economy. I definitely concur with this - and I think Cowen would too - what I think these critiques are missing is some sense of proportion. Sure these problems could emerge - but are they more serious than the additional unemployment that would result from the deficiency in demand that you're going to see if mass layoffs across sectors occur? In other words - how would you rather malinvestments be liquidated and reallocated: (1.) all at once so that everyone is searching for a job at once in an environment where nobody wants to buy anything because they're all looking for a job, or (2.) slowly over time because of business cycle smoothing which allows malinvested workers to look for better opportunities in an environment where we don't have five or six job seekers per job and in which there is not as great a deficiency in demand. The Rizzo/Catalan position seems to assume (1.) is best and that if you don't do (1.) malinvestments will never get a chance to work themselves out. I just don't see why they see it that way. And their general aversion to talking about effective demand and related aggravating factors seems to prevent them from being anchored in any real sense of proportion or sense that we're facing very real tradeoffs here. Rizzo is right that you can commit fallacies when you rely too heavily on aggregation, and his critique of Cowen is exactly right. But you can also commit fallacies when you rely too heavily on inferring up from microdata - and Rizzo needs to remember that.
A lot of these discussions go back to a post by Steve Horwitz on the specialization of labor. I obviously agree with this point - specialization and exchange is what makes the modern market economy. But I'd raise one qualification (I also have comments on the post): I think people involved in this discussion have been far too cavalier about equating jobs with workers. My reading of the literature is that jobs are more specialized today, but workers are less specialized. I'm not so sure what the implications of this are, but a lot of people are editorializing with the implicit assumption that both workers and jobs are specialized. This seems to make some of the fundamental questions of the Cambridge Capital Controversy more relevant - specifically questions about "reswitching". I haven't thought all this through, but I think some of these details can be very important. The labor market is a matching game, and we need to keep in mind both ends of the match (this is why I think gross labor flows an labor dynamics are so important to macroeconomics, and why I want to build a research agenda around that if I ever get into a doctoral program).