There are plenty of good solid stalemate breaks there. Let's see, your turn 13: you had a 4 card deck of 2 Stewards, 2 Pirate Ships. Your opponent had no draw pile. Your correct move was:
Steward: Trash either Steward x1, PS x1 or PS x2, probably the former.
Buy: Copper.
You now have a 3 card deck: Steward, Copper, PS. You are immune to Pirate Shippery, since you have no draw pile.
Next turn: Steward or PS for +$2. Play Copper, buy Silver.
Your deck is now, Steward, Copper, PS, Silver. Still immune to Pirate Shippery.
Next turn: Buy another Silver. You can attack your opponent with PS if he's trying to get out of the hole, here, since you've got an action free.
Your deck is now Steward, Copper, PS, Silver x2. Still immune to Pirate Shippery.
If your opponent is waiting and not doing anything here, I think that the right answer is now "Steward: trash Copper & Pirate Ship, play Silver x2, buy Bureaucrat."
At that point, you've got a deck which is Steward, Bureaucrat, Silverx2.
Next turn, you Bureaucrat, and then buy another Silver. When you're reliably gaining 2 better-than-Copper treasures per turn, your opponent is pretty screwed (and you'll be doing that pretty reliably until your deck reaches a large enough size that Bureaucrat is unlikely to be in your hand). He can PS to attack you, but you'll still be gaining Silvers all told. If he converts to trying to use his PS for money, you increase your Treasure stockpile still further.
Alternately, if that concept of that gives you hives, once you've got the Steward & 2 Silvers and a small deck, you can buy a Mint, trashing your Silvers, and then, keeping your deck size below 5, get a Gold. Trash your Silvers and Mint up a deck that's Steward, Mint, Goldx3, and then do the same plan as before, except instead of Bureaucrating Silver, you Mint Gold.