Honestly, this is just another situation where what Bioware spews out just doesn't make any **** sense. If the Krogan really did reproduce 1000x faster before the genophage, they would have completely destroyed their ecosystem long before nuclear weapons came into existence. Even now, they manage to maintain a(slowly diminishing) population of several billion on Tuchunka, and it's stated that they don't even have much in the way of agriculture, so what do they eat?
If their population really is slowly decreasing, then if you even *doubled* that birthrate(2/1000) then they would be able to sustain their population and grow at roughly 'normal' levels(by other species' standards). So how could they possibly have evolved to naturally have a thousand times their current birthrate? Were 999/1000 krogan REALLY eaten by thresher maws? And just how fast do the plants on Tuchunka process organic matter? If a single Krogan weighs 500 kg, that means that in order to maintain a stable population you'd have literally PILES of bodies lying around at any given time. It would be impossible to bury them; each living krogan would have to bury hundreds of their kin each year! Do they just dump them into piles and let them rot?
And, frankly, it doesn't MATTER whether or not they have clutches in the thousands. It's enough that they produce vastly more offspring than any other species in the galaxy and live for a thousand or more years. With no deaths attributed to age, exponential population increase quickly takes hold and pretty soon you've got quintillions of krogan rampaging through the galaxy.
Basically, the whole **** idea doesn't make any **** sense. You can have long lives or you can have high birthrates, not both, not unless you want an apocalypse.