What should I do differently on this board?
Hi luser,
Your draws are pretty unfortunate here. Not drawing your chapel on t3/4 is always a huge setback.
However, your plays could still be improved.
First of all, there is this point: The 'golden deck' you eventually built (2 King's Courts, Monument, Bishop, Provice) scores 10 points per turn, without ever getting worse. In 'your average game of dominion' that is a lot, easily enough to win. However, this here isn't an average game. You can score so much because there are some strong cards in the kingdom, and your opponents can use them too.
Just adding more king's courts, monuments and/or bishops would not help your deck at all: they would just sit there in your library. What you really need is cards that draw more cards. You could add any number of Peddlers and some Rabbles.
Comments on your actual game: try to focus more on cleaning up your deck. You want to trash as many cards as possible, and the usual danger of trashing too much is almost completey nullified by the quarry you already have. Cards like Monument and Bishop get in the way of playing a big chapel.
After that, you need a festival so you can start adding Peddlers and King's Courts.