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The strategy also lies in the building order (or ignoring buildings at all). Also, the problem of "fixing" happiness is absolutely non-trivial - if you want the best solution. I can tell this, because I even wrote a script to calculate the perfect solution. You would be surprised how complex this script is and what solutions you don't see. With this I did easy in 81 turns, normal in 96 and impossible in 145.

Wow! I'm interested in this script, I thought that optimal water distribution was NP-complete!

I managed impossible without selling anything, but it was soooo difficult to optimize water distribution every turn to grab that one extra influence or two each time.