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I've noticed that those who study self-regulation nearly always include some phrase like "this species has evolved a means to avoid overpopulation".

Now there's pretty much only one way anyone can believe this: everything that exists evolved, so this mechanism evolved. But they don't seem to have given it any more thought.

Consider what's supposed to have evolved. Consider it carefully.

Once upon a time, the species has no regulation. Reproduction is full-throttle, all the time. One day, an individual emerges which by some means or another is equipped for self-regulation. When the population density rises, this individual stops reproducing. The rest keep going & going. They overpopulate, struggle, etc. Meanwhile, the self-regulating individual goes extinct. The trait is removed from the population.

I know evolutionists & their faith in luck. Some will say the SRI could get lucky & survive. So what? The cycle just repeats. Round 2: SRI & offspring will again stop reproducing, forfeiting the field to the competition. How many cycles can they survive? Rigid evodoctrine calls for extinction in the very first round, but even loosening up the Darwinism can't account for cycle after cycle.
Perhaps. However, in complex situations like species interactions, no matter how simple you want to be, there is usually no simple answer.
The aggressive behavior could have existed first and the reduction in birth rate could have been a trait later. The reduction in birth rate could have helped a group of ancestors of all these rodents survive geographically isolated from the rest of their species. Then when the others had starved off, the now predominant individuals could have had sway in their ecosystem.

I agree that my suggestions above are conjecture, but so is your simple conclusion.

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The trait in question must exist from the very beginning. It cannot arise, compete, and survive in a population that does not possess it. It's very nature is to not compete, and not pass on to future generations.
You act as if the reduction in birth rate is a complete stopping of the birth of all lemmings. None of the papers and articles that you provided say anything like that. In fact they point out that the birth rate reduces below the losses due to predation, sickness and the like; it doesn't stop.

A faith that connot survive collision with the truth is not worth many regrets. -- Arthur C. Clarke