Engine is the correct call. It is a long game, but most of your purchases looked reasonable to me. The turn 4 Throne Room could be questionable, maybe should be a Masqerade or second Witch. One thing to consider in a Conspirator deck with weak draw is that Gold becomes a weak card (it is a dead card for drawing your deck). I'm not sure you want any here, although one is probably okay. I certainly wouldn't try to activate the Market Square reaction, they are still very useful here for +buy and Conspirator chains though.
Another thing to think about: once you see that your opponent is not building an engine (and is even ignoring Witch entirely) you should give preference to Masquerade plays over Witch at the start of the game. So Throne Room the Masquerade if you have a choice between it and Witch, play Masquerade over Witch. Trash your deck down quickly, then you will be able to draw your deck more consistently, and you will end up putting the Curses in your opponent's deck faster, while you also decrease the chance that he will pass you Curses with your Masquerade plays. I am not 100% sure on this piece of advice, but I think it could be correct, and it seems interesting to me since people usually try to play their Witches as early as possible.