Hah, I knew it was possible to do better, 7 more cities by turn 3 is incredible. I guess you'll be finishing in 10 turns instead of 10 years.
I never really tried that thin line concept nor that camping in the corner idea to reduce being flanked and usually felt my Hoplites definitely had room for improvement (well I guess I have the improvement right in front of me).

Regarding Corinth, I didn't dare touch it on turn 1 as the garrison had a unit of Archers in addition to 2 Militia Hoplite units and a general and everyone knows archers + stone walls = big time casualties when you are in a straight rush to beat the time limit.
So I had Kleomenes take Kydonia first which wasn't really easy either and in fact cost me a number of Spartans. When I returned to the mainland on turn 3, the Archers and 1 Militia Hoplite unit had left the Corinth to take Athens(?) or travel to Larissa. So I guess you could say I got lucky.
Without Archers, Corinth can be taken without too much trouble. You just need to select the best place to put the siege tower and then rush in with all speed. They'll probably place the Mil.Hops on the wall but Spartans can take out Mil.Hops without problems even on VH so it might be tight but it's doable.

Maybe I should try Spain next. Crap infantry, crap cavalry, no archers and doesn't have a booming econ like the Greeks. Sounds like a bummer already.