With 6 cities, I've been aiming for 8 natural GS. My approach has usually been to aim to get 2 GS from the cities with an extra GPP from Great Library and Oracle, most likely the capital and a strong expo. I aim to finish LToP shortly after the 2nd GS, so that city will need to produce 200 + 900 = 1100 GPP. That means, if buying Universities but not in the GL/Oracle cities, it's best to wait a few turns, so the expo with the purchased University doesn't end up producing a GS first. If purchasing in one of the GL/Oracle cities, then it would be okay to purchase in a weak city right away (typically the weakest city that won't have a garden).
Ideally, all cities are planted quickly and you can pick up a couple Maritime CS allies, in which case purchasing Universities isn't necessary (especially given there's most likely no discount). If that looks like it's going to be the case, a Granary in the last city or two might be one of the best uses of early gold.
With a stronger start - 6th city planted before T35 - I've trimmed it down to a T147 finish. I planted a 7th city later as well. Faith bought 2 GS and 1 GE, as I wasn't going to make it to 5,000 faith. I don't think I got enough gold out of the 100 per city to make it worthwhile, given that the comparison with Tithe (and little to no active spreading) needs to factor in faith from planted prophets. Worth considering: how much gold by Plastics (from faith) is equal value to a 3rd faith GS? 1,000 gold? 2,000 gold?
3,500 faith is relatively easy on Settler, with the 2 faith per wonder and Reliquary. Planting prophets puts you in a better position to hit 5,000/6,000 not only from their output post-Industrial, but potentially accumulating more before Industrial.
My main error this game was not generating enough culture and only taking the Commerce opener, which led to building more schools/labs than I'd like. Putting some gold into Cultural CS (earlier) would have paid itself back and more in the long run with Merc. T123 Plastics, but I lost value on the bulbs up to Apollo due to getting Labs up late, so it took 24 turns from Plastics to finish.
I think a key factor to taking a significant chunk off at this point will be producing an 8th natural GS before T140, which comes back to getting those science buildings up immediately through gold or faith purchasing.