I assume the "I own only differently named kingdom cards" in the puzzle description applies at all times, so you can't during your turn get a Kingdom card you already own.
I can't find the last thing you talk about, but I've found a few cards that help and I've fixed my mistake. I can now get: 61
In the beginning you have Caravan Guard (played on your opponent's turn), Hireling and Champion in play.
Then you call Ratcactcher, Guide, Transmogrify and Teacher.
Then you play your Princed King's Court and play Golem, playing 6 action cards and calling Coin of the Realm and Duplicate. Call Royal Carriage to play King's Court again. This time you play Throne Room, Procession and Herald, playing 2 cards. 2nd Procession plays Band of Misfits as Herald, playing 2 action cards. 2nd Throne Room plays Disciple, and you play play the other 4 Disciples too (note that the puzzle only states no Kingdom card duplicates, and Disciple isn't a Kingdom card). With that you play Graverobber (gaining Herald and Band of Misfits from the trash), a drawer, Herald (playing 2 action cards), Band of Misfits as Herald (playing 2 action cards), 2 action cards, and Black Market, which plays all the Treasure cards in the game (you've earlier played a lot of non-specific action cards, which may be drawers, and you have a +1 card token, so drawing the treasure cards isn't a problem).
The last played Treasure card is Spoils, and while you resolve that it is the start of your turn and you count your different cards in play: Caravan Guard, Hireling, Champion, Ratcatcher, Guide, Transmogrify, Teacher, King's Court, Golem, Coin of the Realm, Duplicate, Royal Carriage, Throne Room, Procession, Disciple, Graverobber, a drawer, Herald, Black Market, 26 treasure cards* and 16 other action cards for a total of 61 cards.
*Copper, Silver, Gold, Harem, Potion, Philosopher's Stone, Loan, Quarry, Talisman, Contraband, Royal Seal, Venture, Hoard, Bank, Platinum, Horn of Plenty, Diadem, Fool's Gold, Cache, Ill-Gotten Gains, Spoils, Counterfeit, Masterpiece, Stash, Relic and Treasure Trove.