Your execution seems to be mostly fine, but I would get more Shanty Towns early and I would play no more than 3 Wharves every turn because if you play more than 3, the next turn you have to play less than 3, and then you get turns like turn 16.
I would actually go for the BM here. Wharf+Masterpiece is very strong, and with Shanty Town as your only village and no trashing, the engine is slow. Your opponent misplayed it a lot — he shouldn't have bought a Cellar, he shouldn't have bought Shanty Towns and he should have gotten more Masterpieces early.