I feel I should comment on my strategy, because it's a good example of developing a strategy, and I think it's actually the best strategy on the board, even if it does require a good deal of luck to hit 12 turns.
The obvious part is the draw engine. The only way you're going to be able to draw all those cards is Apothecary/Wishing Well. Vault just doesn't draw enough cards. Then there is the matter of how you're going to build the engine. Since there is no +buy, the only way to get enough Wishing Wells is with Workshop.
Then you also have to consider the payload. Since there is no way to get more than one VP card per turn (excluing Estates), the goal should be $11. You can do this with Plat or Coppersmith, each of which can buy a Colony when combined with 6 Coppers. Each has its own advantages and disadvantages. Platinum doesn't require an action, but it costs more, so you have to get either 2 more Coppers or a Silver. Coppersmith requires an extra action, but its cheap enough to be gained by the Workshop. All things considered, Coppersmith is the clear winner since there is no +buy to get 2 Coppers, Village is going to help your deck while Silver hurts it, and the fact that you can get Coppersmith without a buy saves you a buy.
Finally, is there anything else to add? Well, trashing is a big deal, especially for a very choke-prone engine. If you have 3 Colonies AND 3 Estates, you're going to be in a lot of trouble. Lookout actually fits very nicely with this deck for a couple reasons. First, the Apothecary helps it target down Estates, and second, if needed, it can be used blind to make sure you can get a card you need to the top spot, which I end up doing on turn 12.
Okay, so your deck wants a Potion, Workshop, Coppersmith, Village, and a bunch of Apothecaries and Wishing Wells. What's the order to get them? The natural order is to start with the Potion, since it's your limiting resource. Then the gainer, since it can gain the other cards. Then the trasher, because trashing early is important. And you can wait on the Village and Coppersmith until you're ready to use them. The Village should come first, because it's useful for drawing, and it can allow you to gain and play the Coppersmith on the same turn, as I did on turn 8.
So there's the plan: open Potion/Workshop, get a Lookout and start collecting Apothecaries and Wishing Wells. When you have enough, you can add in the Village and Coppersmith and go to town.
So how lucky do you have to be to get 12 turns? Pretty lucky. I probably tried close to 20 times. The biggest key is getting the Potion back early in the shuffle (turn 5) so you can get the Apothecaries fast enough. Otherwise you're going to cycle to slow to make it in time. Then you just have to hope for no terrible draws like a hand of all Copper, which is not that unlikely with 6-7 Coppers in the deck.
Powerman commented that I was unlucky to not draw the Coppersmith on turn 9, and that 11 turns is possible, but I think you'd need to get *really* lucky to actually hit 4 straight turns on 3 Apothecaries. The turn 9 "miss" allowed me to get a 4th, which made it easier to hit the next 3 turns. So sure I think 11 turns is doable, but would probably take too many tries to be worth it.