Well I'm out of town again so I won't be able to tell the turns for the various victories for a while. Seeing how the game was playing when I saved on turn 171 (point in time when I had to pick between science/diplo/total dom), I expect diplo win in the 180-190 range which would be over 30 turns faster than my current best deity diplo. Probably 250-260 ish for domination since I didn't do any kind of rush 'till artillery(wasn't originally planning on dom). Science I am somewhat unsure since there are so many techs away but I guess 245 is a good estimate - 2 Waves of RAs, 6 different bubbles and enough cities/hammers to build the parts easily.
As for comparing the games. I play on deity and even though I don't play/post for HoF, I still always play in a competitive perspective thus any games which I compare the above with didn't have any negative bias to prove a point or anything.
The issue in your idea of "making up for that much culture, etc" is that the exponential cost increase on SPs kinda solves this by itself. By this, I mean that even if you do produce less culture early in the game even to the point where a given start has 6 SPs on turn 100 and the other game only has 4 SPs on turn 100...is that the gap between the two games will slowly catch up to the point where there is really only one SP difference and sometimes "less than a full SP". As such, if your worse SP gives marginal benefits, then you have gained close to nothing from having one more SPs.
I kind highlighted that idea when I proved doing tradition->liberty->citizenship->meritocracy was very awful compared to liberty->citizenship->meritocracy UNLESS you intended to go deep into tradition for LE (or say played shongai for 4 mud pyramid mosque).
Ultimately, the reason why hoarding SPs is more powerful than opening any of the 3 trees is because of the broken scaling of scholasticism at higher levels. It is commonly agreed that NC start is the most reliable mean to help catch up AIs some (they start way ahead due to initial bonuses on emperor+). It is not the only way to go, hard early REX can do fine if you can survive the wars but NC is the most played/most reliable/works with nearly every strat.
Now a standard NC start will get you to 30 or so BPT around turn 60 and then very slowly increasing to like 40-50 BPT around turn 120 depending on how much you REX and how good you is your growth. Unless you play france, GE rushed stonehenge and spent all your gold on cultural CSs, a 6 or 7 SP lineup to get scholasticism won't ever come before turn 120 (and that's very generous). In the very example of my played game hoarding SPs, I unlocked scholasticism on turn 68. At the time, my BPT went from 38 to 85. This is fine renaissance science production obtained the very turn I entered medieval. I could've likely just saved the game there, given it to king/emperor player who never beat deity and watched him plow through it easily...
Being Tech leader is the better way to win any strat - also why most competitive players vote babylon as the best all-star civ. One of the reasons why deity is so hard is because of how much you need to catch the AIs tech-wise. Turn 70 scholasticism with decent gold managing will push you much, much further tech wise than anything else you could do.
Anyway Joseph, I don't know what difficulty level you play but if it is king+, I suggest you try to play a game where you try hoarding SPs to scholasticism (prince, the CSs BPT production is alright but not significant to the point of leveraging a game). You will have to adjust your standard opener to build worker and purchase/build settler but as soon as you pop scholasticism and have a few CS allies you'll clearly see my point
