Hearthpwn

Getting to play Quest Priest with quick games and a guaranteed curve is pretty darn great, and I've yet to lose a game with this deck! I've made a lot of modifications to this list compared to the typical list meant for Standard ladder play, because this brawl makes the deck play quite differently. 

First, you don't need redundancy of mana costs because you're guaranteed to draw cards on curve. Those on-curve cards should be a) playable regardless of the board state so that you can always play on curve; b) focus on survival or disruption since you already have extreme inevitability; and c) not generate extra cards because you don't want to over-fill your hand. I did make sure that there were at least 2 cards for each mana cost in order to avoid being foiled by an opponent's Theotar, the Mad Duke or Mutanus the Devourer. 

Second, you want everything besides your curve cards (which should be playable regardless of the board state) to be 0- or 1-mana spells. The cheap spells can help you heal and clear minions. You can fit them in while still keeping a perfect curve with coins (from Mailbox Dancer), with Priestess Valishj, or on turn 9 when you play the quest reward Xyrella, the Sanctified. (There is no other 9-mana card, because you should be playing Xyrella, the Sanctified on that turn instead.)

Finally, you don't need ways to find the Purified Shard (like Sir Finley, Sea Guide or Thrive in the Shadows), because on turn 10 you're already guaranteed to draw the Purified Shard and end the game! You actually actively don't want to draw the Purified Shard early, because that gives your opponent a chance to Theotar it out of your hand.

Note that if you are late to finish the quest, it's not a big deal because you're still guaranteed to draw the shard. That said, I found it best to just play cards on curve in all but the most extreme of situations.

Notes on card substitutions: 

0- and 1-mana slot: Priestess Valishj and Gift of the Naaru are nice but not necessary for the deck to function. Try Call of the Grave instead, or maybe even Focused Will or Irondeep Trogg!

4-mana slot: Blademaster Okani and Theotar, the Mad Duke help you slow down your opponent and throw them off curve or disrupt their game plan. If you don't have those legendaries, however, Holy Nova is also an option. Or you could put in 2 Lightmaw Netherdrakes, but you'll need shadow spells to go with them. Try 2 Call of the Graves instead of 1 Lightshower Elemental and 1 Lightbomb and 2 Thrive in the Shadows instead of 1-2 Holy Smites (and/or 1 Mailbox Dancer). 

6-mana slot: I included two Lightshower Elementals and two Lightbombs because they're useful in different situations and this increases the odds that you have both to choose from on turn 6. But if you want other cards anywhere, this is a good place to cut!

7-mana slot: Blackwater Behemoth and Mutanus the Devourer are harder to replace, but you could use Red Herrings or Humongous Owls. I probably would not use Elekk Mounts, because you might not have a minion on board to buff. If you really want to use it, probably take out the two Lightbombs to just leave yourself with 2 Lightshower Elementals and make it more likely that you have a minion on board on turn 7.

8-mana slot: Whirlpool is helpful (even though you probably just played a big minion on turn 7!) since you're not really trying to build a board and people tend to have lots of big minions in this brawl, but Mo'arg Forgefiend also works.