I'd repeat my point about the developing countries not being that primitive anymore. In fact, I do believe most of them had an explosive population only after greater technology was introduced. That's sort of what I was getting at
Secondly, I think you overestimate the dependence on funded education and underestimate the diffusion of knowledge. 5 year olds today know far more than they did 1000 years ago. Information becomes common, and as such, people pick up more and more of it earlier and earlier, without much cost. Certainly not more cost than the technology itself can make up for.
Except I never said anything about their technology coming back, I said a permanent blackout, so I think their capacity would be lower than 6.7 billion and their growth rate may be slower too, though that's not important. I think maybe I need to emphasize the difference between a growth rate and a population capacity. The former can be high even when the latter is low.
And as you said, it's an S curve. However, I do not think that hyperbolas phase leading up to the mid-twentieth century or so was caused just be the development of agriculture. Going from 1 billion to 6 billion in a 100 years, I think the industrial revolution had a lot to do with it.