Small little exploit I managed to find that you can use on the first boss...
If you draw in Dungeon Run you have to redo the stage you're on. It turns out that if you can force a draw on the very first boss by killing both heroes with Hellfire, you get taken back to the first boss screen with your Warlock deck displayed on the side, but when you click Play the game asks you to pick a class. It takes the new class you pick and the corresponding hero power and puts it with the base Warlock deck.
Note that once you complete the first battle, your hero and power update back to Warlock, so this isn't actually useful beyond the first boss unfortunately.
Screenshot
After a bunch of experimenting I found out you can get the same first challenger twice in a row, not sure whether this applies to later stages.
https://www.reddit.com/r/hearthstone/comments/7zkdsc/using_drawtie_mechanics_in_dungeon_run_to_combine/