The above qualitative analysis is sufficient to strongly suggest that six months is an unlikely high-end estimate for time required for take-off

We've been using artificial intelligence for over 50 years now. If you haven't start the clock already, why not? What exactly are you waiting for? There is never going to be a point in the future where machine intelligence "suddenly" arises. Machine intelligence is better than human intelligence in many domains today. Augmented, cultured humans are a good deal smarter than unmodified ones today. Eschew machines, and see what kind of paid job you get with no phone, computer, or internet if you want to see that for yourself.