I've opened double Curse and won before
So I'm pretty sure you screwed up here. Towards the end, on one turn you had Remodel, Horse Traders, a couple Provinces, and some money in hand. You remodeled a Silver into a Duchy, then bought a Province. Instead, you could have played Horse Traders, discarded the Provinces, and had $13 and 2 buys, to buy a Province and a Duchy. Same result except you have 1 more Silver in your deck, which you really could have used in the turns after that.
That, and I'm not sure your opening was optimal.