It happened in the real world, ergo the issue lies with your understanding of the system we're talking about and not with its inability to conform to your model.
I've heard claims like these several times, but this situation where individuals voluntarily limit their reproduction for the common good can't possibly be a stable equilibrium.
You're looking at this backwards. This is the reproductive context in which humanity evolved, and the Malthus-driven upward spiral of population and competition is the result of comparitively recent cultural shifts brought on by changing lifestyles that made it viable to do that. You don't need to invoke group selection in the form you're thinking of -- the cultural "mutations" you're positing can't gain a foothold until some branch of humanity has access to a lifestyle that makes it advantageous to defect like that. Forager societies don't have that incentive because if they overtax their resource base here and now they have to move, and for most of human prehistory (and the modern history of hunter-gatherers) the population densities were low enough that this gave the affected area time to recover, so when someone came back, things were fine again. A long-term climatic shift alters the range of viable habitats near you, but it takes something pretty darn catastrophic (more than just a seasonal or decadal shift) to entirely render a region uninhabitable to a group of size n.
The biggest filters to population growth in this system are entirely passive ones dictated by biology and resources -- the active ones are secondary measures, and they're undertaken because in a system like this, the collective good and the individual good are inextricably linked. It was a stable equilibrium for most of our evolution, and it only broke when and where agriculture became a viable option that DIDN'T immediately overtax the environment.
That's a state of affairs that took most of human existence to come into being.
It happened in the real world, ergo the issue lies with your understanding of the system we're talking about and not with its inability to conform to your model.
You assert these things very confidently, but without any evidence. How exactly do we know that this state of affairs existed in human prehistory?
You say:
...You don't need to invoke group selection in the form you're thinking of -- the cultural "mutations" you're positing can't gain a foothold until some branch of humanity has access to a lifestyle that makes it advantageous to defect
From Mike Darwn's Chronopause, an essay titled "Would You Like Another Plate of This?", discussing people's attitudes to life:
Conclusion, graphs, and references in article. As usual, I recommend reading Chronopause.com as Darwin has many good articles; to quickly link a few: