Festival, market, lighthouse, fishing village, minion, and similar cards. Anything that adds as much value as silver and lets the jack look at the top of the deck then draw up to 5 cards. A scheme with a jack is better than two jacks. Venture, bank, royal seal, stash probably work really well. The simulator also seems to prefer a variety of Jack + other over two jacks, with a variety of other such as council room, monument, rabble, harvest, witch, merchant ship, even oracle.
Most trashers probably aren't needed and offer minimal benefit if any.