Hmmm, Corinth's design is kind of...odd, because you very clearly have a UA and UB (and to an extent, UU) that would be fantastic for expansion, only you can't found extra cities. A temple that gives extra Happiness isn't that useful with only one city, and even if you conquer things to make better use of it, puppets don't use specialists IIRC so you're looking at a UA that culminates in an extra +6 GPT and +8 production in one city by the mid to end game, and is nonexistent until well into the medieval era.
I would consider re-adjusting things! You've got to have an extremely potent set of abilities if you're working with an inability to choose where you settle - Venice gets double capacity on the backbone of economy in BNW and can basically take city-states, which is very powerful if you know what you're doing. Periander was one of the Seven Sages of Greece and a big patron of writing: the most obvious thing to me is a simple 'expending Great People not making an Improvement provides double their bonus', and maybe, say, a unique Writer's Guild that has twice the amount of specialists? Or simply have the UB do what it does but also give GW points in the capital.
trade route to your cities, 10% of the city's 
gold output is converted to 
production. 'We love the king day' increases building 
culture from buildings in the capital. May not 
annex cities, and settlers found 
puppet cities.
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