I played through a couple of different options to see what difference loitering makes. There's a bit of a tradeoff between say a 10-pop T13 switch to Harrapans and a 20-pop T21 switch to Egypt.
Very interesting experiment, and mirrors the things I am trying out these days. So I also want to try to combine staying in Neolithic as long as possible, but to still grab Harappans. That means transitioning around ~turn 10-11 in my experience. I find that I can usually get 9-10 pop and most of the time get the knowledge star also (but not reliably in such short timeframe, which i consider a real loss). I find the mammoth population can vary considerably depending on luck, so it's hard to really rely on it for influence.
My last game I went ancient turn 11, second city was up around turn 18 which is pretty fast, but I focused on second city before attaching any territories (so ~50 less influence required). Not sure if that is optimal, but the yield I really want to maximize after establishing a city is influence. One thing you are perhaps leaving out of the equation here is influence from curiosities in ancient age. With a horde of scouts or runners moving about, you're bound to find rather a lot of them at 8 influence each? That does, IMO, shift the balance a bit in favor of transitioning earlier (to get better results) but of course you need enough scouts to cover the ground.
So I think for Harrapans, you need to transition around turn 10, no way around it, but you can still grab a decent size pop and the knowledge star if you play tight and have some luck. For a delayed Egyptian transition, it might be that turn 20 is a bit on the late side? The real payoff probably lies between the accelerated influence gain from having a city + pottery + increased curiosity yield (favors quicker ancient) vs. gaining more pop/scouts (favors neolithic).
It's a good thing for game balance that there is a tradeoff

What we probably can conclude definitely, is that going ancient before turn 10-11 usually is not optimal, as that means you are not exploiting neolithic enough for pop and the legacy, nor are you likely finding the optimal city sites. Turn 20 might be on the high side as then you are not exploiting the ancient bonuses early enough, and turn 10-ish is the goal to grab Harrapans.