Your belief that something like present technological advancement could continue after a cataclysmic collapse boggles my mind. The one historical precedent we have - the Dark Ages - teaches the exact opposite lesson.

IIRC, Robert Wright argued in his book NonZero that technological development had stagnated when the Roman Empire reached its apex, and that the dark ages actual brought several important innovations. These included better harnesses, better plows, and nailed iron horse shoes, all of which increased agricultural yield. The Dark Ages also saw improvements to water-wheel technology, which led to much wider use if it.

He also makes the case that all the fractured polities led to greater innovations in the social and economic spheres as well.