We should not assume that the best what a civilisation has would be preserved after a collapse (or mere culture change). For example, there is a theory that Hellenian Greeks made important breakthoughs in technology, formulation and application of scientific method, but they knowledge was not preserved beyond Roman conquest, since only most practical and easily understandable works were partially preserved.

As for post-collapse period of our civilisation, I put up a scenario in a parallel diary.