4 Turns.
Turn 1: Draw 5c. Buy Band of Misfits
Turn 2: Draw 2c, Shelters. Use Coin Token (Baker start), Buy Menagerie.
Turn 3: Draw Menagerie, BoM, Overgrown Estate, Necropolis, Hovel. Play Menagerie draw 3c, Play BoM as Remake, Trash Nec, Gain Estate, Trash OE, Draw Copper, Gain Estate, Buy Estate, Trash Hovel.
Turn 4: Draw 3 Copper, BoM, Menagerie. Play BoM as Island, Set aside Menagerie.