Bulbing Civil Service seems like a good idea then. Can we really get a scientist from Riverdale before the capital overtakes it again though without running less specialists than we'd like to in the capital though? The capital will have 2 scientists worth of gpp just from wonders. Maybe The Great Library could be built in riverdale? Although it's such a tech detour to get it that it probably won't help until we're popping scientists to get education or some such. Still, with the Pyramids and the philosophical trait it's a great wonder to pick up.
Let's work out the Math.
The capitol will have The Oracle (2 GPP) + The Pyramids (2 GPP) = 4 GPP / turn
If the capitol also runs 2 Scientist Specialists, at 3 GPP each, 2 * 3 GPP = 6 GPP / turn + 4 GPP / turn = 10 GPP / turn * Philosophical Trait bonus of 100% = 10 * 2.0 = 20 GPP / turn
Riverdale will have 2 Scientist Specialists, at 3 GPP each, 2 * 3 GPP = 6 GPP / turn * Philosophical Trait = 6 * 2.0 = 12 GPP / turn
The 1st Great Person requires 150 GPP
The 2nd Great Person requires 300 GPP
The 3rd Great Person requires 450 GPP
The 4th Great Person requires 600 GPP
If Riverdale is to produce the 3rd Great Person, it needs to accumulate GPP for 450 / 12 = 37.5 turns. However, that's 37.5 (actually 38) turns AFTER we have completed the Library. In my test game, I was building Cottages, but I could instead focus on chopping out 2 more Forests, in order to get the Library about 10 turns from when The Pyramids are complete, with 4 population points in Riverdale.
So let's be safe in that number and say 50 turns after we build The Pyramids is the EARLIEST that Riverdale can generate a Great Scientist.
If we try for a Great Scientist as our 2nd Great Person in the capitol, we can get a Great Person in 11 turns after building The Pyramids, by immediately hiring 2 Scientists. Just because we TRIED for a Great Scientist doesn't mean that we will get it. But we'll have a use for the others--Civil Service for a Great Prophet or an "instant Apostolic Palace" with a Great Engineer. I don't worry about not being able to generate another Great Engineer later, by the way, and I do not think that it would be wise to let our 2nd Great Person "sit on ice" for most of the game.
Anyway, if we don't get a Great Scientist then, we can keep pushing to get one in the capitol or else we can reduce the capitol's Great Person production and aim to get one for certain in Riverdale.
It would take us an additional 450 / 20 = 22.5 turns to get it in Delhi.
So, in a span of 11 + 22.5 (really 23) = 34 turns after The Pyramids are complete, we can have 2 shots at a Great Scientist in Delhi. Should we have failed the first time, we can grab Civil Service and then Alphabet, as Alphabet is required in order to Lightbulb Philosophy.
3rd Great Person--from Delhi?
Let us say that we will end up with our 2nd Great Perrson as a Great Prophet no matter what we try to do (which is highly likely, even with 2 Scientist Specialists being hired, since The Oracle has been putting in Great Prophet GPP for a long period of time). Should we try for our 3rd Great Person from Delhi and should it fail to be a Great Scientist, then we'll just manually plug away at Philosophy. If we get a Great Prophet at that point, we'll probably settle him (we don't want a Holy Shrine, as getting one spreads religion), and we'll settle him in either:
a) the capitol, for increased Wonder production
b) our Great Person Farm, to help build a Granary, a Library, and the National Epic
A relatively-early settled Great Prophet adds good value, due to the extra production that he supplies over his lifetime. The Gold boost from a settled Great Prophet usually equates to having the Holy Shrine of a poorly-spread religion. Remember, in this game, we want all of our religions to be poorly spread in foreign Cities, or else we will just be tempting the AIs to switch into Free Religion, so we won't have the alternative of a "well-spread" Religion's Holy Shrine.
3rd Great Person--from Riverdale?
50 turns after The Pyramids, say, even 60 turns, in case we need to irrigate a Flood Plains square, we should be able to complete our Library, hire 2 Scientist Specialists, and complete a Great Scientist.
Maybe.
If Zara truly is building The Great Wall or Stonehenge, which would make sense due to his settling delay, then we might not get a 4 Food square in time. So, we can't 100% plan on this approach, in case we can't get the Cow or a Flood Plains square in time, as you need:
2 Grassland Farms and 4 population points for 1 Specialist
4 Grassland Farms and 6 population points for 2 Specialists
1 Grassland Cow or 1 Flood Plain Farm and 3 population points for 2 Specialists
Clearly, Food is king.
Should we happen to end up with extra population points above those numbers (it will be hard enough achieving those numbers as it is!), then such an extra Citizen can just work a Grassland Cottage or an Irrigated Plains square, without disrupting the results of the numbers.
Thus, we won't be able to get the 3rd Great Scientist from Riverdale without a 4-Food square, plain and simple.
If we don't get a 4-Food square within a reasonable time frame, then we will need to pour our resources into cultural buildings in Riverdale until we do obtain one.
The Results of the Calculations
So, when doing the math on the subject, yes, I think that we should try for a Great Scientist from our capitol instead of from Riverdale as our 3rd Great Person.
But what about our 2nd Great Person? Early Bureaucracy would be really amazing.
However, we can mitigate the risk of missing a Great Scientist as our 3rd Great Person if we try to get a Great Scientist for both our 2nd and 3rd Great People from Delhi.
If we were to hire Science Specialists in the hopes of getting a Great Scientist as our 2nd Great Person, and should we be successful in getting a Great Scientist, we can next fire the Scientists and hire Priests in Delhi, getting Civil Service 23 turns later via a Great Prophet as our 3rd Great Person. That would be the price for increasing our chances of securing Philosophy via a Great Scientist.
Of course, should we get a Great Scientist for our 2nd Great Person and then TRY for a Great Prophet as our 3rd Great Person, we could also end up with a Great Engineer for our 3rd Great Person, which would mean that we'd have to keep trying for a Great Prophet as our 4th Great Person and that Bureaucracy would be greatly delayed. Perhaps we could speed things up a bit at that point with the help of a Temple from a 3rd Religion, giving us an extra 6 GPP / turn, as well as 4 GPP / turn by building the Apostolic Palace using the Great Engineer in the capitol, but Bureaucracy wouldn't be early at all anymore.
The alternative is to AIM to get Civil Service about 11 turns after completing The Pyramids. Early Bureacracy (an extra 23 turns of it) is potentially worth having to manually research Philosophy. In the meantime for those 23 turns, we will have a choice:
a) Beeline Alphabet -> Philosophy
b) Beeline Alphabet -> something else, such as Aesthetics, to keep the Swedagon Paya out of the hands of the AIs, while saving up some Gold as the 3rd Great Person is about to be born. If a Great Scientist is born, Lightbulb Philosophy, but if one isn't born, use that saved-up Gold to manually research Philosophy