Interesting points, but I think I can answer those too.
First, while the Daughters might wonder what’s going on, they have no reason to guess what’s going on with the First Mother. For all they know, the First Mother is in a situation much like theirs.
Now, let’s assume that this civilization, with the technology of 2027, is forward-thinking enough to keep good records of its medical knowledge and builds good facilities for all purposes: protecting the mothers and children, providing good nutrition and medical care, and storing a wide genetic variety of sperm for the next several generations to use.
Let’s say they can get only get a good 10 healthy, fecund children from the First Mother, starting at roughly age 18-21 and keeping on trying until, say, 46. If they can manipulate the sex of the child in utero, and we assume full or near-full cooperation, then this can be done in no time: 10 fecund girls who can each start getting pregnant at, say, 16, and they can each have 11 or 12 children as a result. [ul][li]So within 28 years, she has 10 Daughters, and several of them have daughters of their own. [/li][li]Within 74 years (which even at today’s life expectancy means a number of the “Old Generation” would still be around), the next full generation of about 115 Granddaughters has all been born, and many of them have daughters, and some have granddaughters. [/li][li]Before you even get to the Great-granddaughters’ generation, you can safely stop manipulating the sex of the children so that when you hit 600 you have a roughly even mix of fecund male and female, and you’ve completed a genetically sustainable population (if I recall correctly that 600 is the minimum number).[/ul] If the first couple generations have contact with the Old Generation’s culture for the first 70-85 years (assuming no gain in life expectancy over today), there’s no gap between the old generation dying and a naturally sustainable population of the new generation.[/li]
Using the stored knowledge and preserved infrastructure of the Old Generation, they should be able to get off the ground without any Dark Age. If the information was stored for them, they could recover the remaining culture that the Old Generation left behind, without having to miss or reinvent it all.
I think this could be done fairly easily with social pressure starting with the First Daughters, without having to resort to actual coercion. Something along the lines of impressing upon them that they have a special responsibility and privilege to be the mothers of an entire species would probably not fail 100% of the time in any generation, I would guess. And as long as there are more sperm samples once the Old Generation males are no longer available, there’s no rush: you’re continually injecting genetic diversity into the population until it reaches the self-sustaining number of 600, at least.
Less than a century and a half isn’t very long in the historical scheme of things, much less the evolutionary scheme of things. Rebuilding to 6 billion people, if they cared to do that, would take a bit longer. But setting things back on a course of growth while preserving our knowledge and culture would be doable.
There’s not a real danger of having to “rape” again unless all the females in a given “fecundity window” are also super-misanthropes, as long as the facilities exist to support the non-misanthropic ones’ reproduction.
This is sounding like a nifty sci-fi novel already. Quasi-dystopia sees a window to future salvation through a narrow window of barbarism, followed by somewhat intense survivalist social engineering and then re-emergence. One of the descendants of the New Generation, now re-emerging into the world and studying the old culture, follows a trail of evidence and discovers the shocking horror that her great-grandmother was repeatedly impregnated against her will to save the species. Drama ensues.