@Percy
I played the first round of a game this evening for you.
I forgot to screenshot the settings, so: Big & Small / Standard size/ Prince / Epic / Random Leader (Gandhi of India).
I'll let the screenshots speak for themselves ... here are the major ones:
I settled in place, because that's just what I always do. First research is Poly for Hindu (and b/c it's a Lit pre-req) followed by Ag & BW. Fast Worker is first build to mine the bare Hill, farm the Corn then chop/mine the forested hills on Settlers.
Lucky break. That hut in my BFC popped for Ag, so now my Fast Worker can Farm before he mines. Just under that tech splash is another hut that's about to pop 3 pissed-off Barbarian Warriors. Bye-bye starting Warrior.
Like I said ... BW is always high on my list.
Bingo! Copper! My first city is going to be either 1N of the Pigs or 1NW of the Copper. I can make a pop 5 city just like this:
City Center = 2 food / 1 hammer
Pig Hill = 5 food / 1 hammer
3 Grassland Hills = 3 food / 9 hammers
Grassland Copper = 2 food / 4 hammers
Total = 12 food / 15 hammers
Who knows what's in the fog ... but quite frankly ... I don't care. +2

/15

at pop 5 ain't bad.
My other city will undoubtedly be somewhere around the Gold and all those Flood Plains as a

farm.
BTW, since I'm Spiritual, I didn't adopt Slavery. The last thing I need is a revolt when I don't even need to be in Slavery.
It gets even better with that Irrigated Corn up there, because even though there's a general lack of early game production tiles (all that Grassland will eventually be Workshops when I get around to CS/SP, though), I can whip down to 2 pop and grow back super fast with +9

off the Corn/Pigs.
I probably won't rush anybody, but who knows, eh?
Just east of the AI's recommended Settling spot will likely become my cottage-spammed Bureaucratic capital city shortly.
I let Delhi grow to pop 4 before starting my 1st Settler for a reason, and this is it.
Now that I can whip the Settler for 2 pop, I'll switch into Slavery and rush it.
2475 BC, and I have 3 cities: Delhi with decent hybrid

/

, Bombay with good

and great whipping (and utterly amazing late-game CS/SP potention) and Vij with amazing food and decent swappable 11

.
I don't love this placement, but it's what I went with anyway. I'll eventually settle a coastal city SW of the Gold for +4

and plenty of coastline to work sometime down the road.
A Granary and Library are top priority in this city. I'll run Max scientists and the Gold mine when CoL/Library comes online.
I'm also banking on there being some decent land SE in the fog I can share the rest of those Flood Plains with.
And here it is: 5 Pop with +2 food & 15 hammers. 16 raw turns for the Oracle isn't bad either. I use the Oracle on CoL and pop Confucianism, which I spread to a neighbor with the Missionary.
Since the Capital has decent production, I'll probably use the Corn to tag team running specialists and Workshops. I have plenty of

resources around, so I'm going to skip HR ... it's health I'll need to worry about.
I got damn lucky and found Iron in Delhi's BFC, so I diverted from a Library and started working towards Military instead. Otherwise, my idea was to have:
City Center = 2 food / 1 hammer
Oasis = 3 food
Grassland Farm = 3 food
Corn = 6 food
2 Grassland Hills = 2 food 6 hammers
TOTAL = 16 food / 7 hammers
That would run the 5 tiles plus 3 scientists ... the Iron just makes it that much easier to run scientists and still have half-decent production (5 hammers & 4 specialists).
If this was a multiplayer game, I'd be dead already. But luckily I'm not. Delhi and Bombay are commited to Settlers, Workers and Axemen now; and Vij is keeping my research afloat (albeit barely...Delhi needs to turn on Scientists soon.) Bombay will build any Wonders I need.
Hammurabi just accepted Confucianism (I sent it to him), and you can see the gears already in motion to build my new capital up north. It'll have a consistent +5 food even while working those Gem mines, and the 3 Grassland hills will let me switch production on/off when necessary.
It's late, so I won't finish this game tonight, but I'll likely expand West and North into Hammurabi and Louis XIV then SE into whoever/whatever is down there.
My research rate will probably slump to 20% as I REX out, but I'll ensure every new city is built to run scientists to help compensate. Shortly after Louis XIV builds the Pyramids (you know he will, since he's the only Industrious civ in my game), I'll take it from him and say "Merci" as he cries for "Mercy".
I'm not sure how helpful that was or how smooth/sloppy that was compared to your games, but this is generally how my games go in the beginning.
My general strategy is to peacefully expand towards my neighbors until there's no more land to obtain. Then I start evaluating my neighbors for conquest or whatever depending on the political climate and what victory I feel like.
20 hammers is a better goal for production cities, but that's hard to do with Grassland Hills -- despite the fact that GHills are more efficient than Plains Hills.