I finished my remaining classes then played more runs until seeing all the rare bosses, then some more with some tips from a guide to see if I can up my win rate. My all-time win rate is 30.7%, which apparently is terrible. Strong players win almost every run:
https://www.reddit.com/r/hearthstone/comments/7i3bbq/twitch_30000_dungeon_run_challenge_announcement/. Dunno why I'm so bad at it. Might be that I didn't quite realize that when you pick a package once, it greatly increases the chances to see that package again. Since some of the packages are way better than others, you can help yourself out by making early picks that promote being offered good picks later. It also seems to be important to anticipate certain bosses as you build your deck.
Overall I found dungeon run to be a fun mode. It falls into the genre of tactical encounters held together by a strategic glue (e.g. X-Com, FTL), and for me, whether such a game is fun depends on how interesting the tactical encounters are. Blizzard must have done a lot of play-testing and tuning, because the boss encounters managed to be non-trivial yet usually winnable, which is hard to do. The places where this didn't quite work out (mostly King Togwaggle) just highlight how well most of the bosses are designed.
Strategically, I apparently missed the point in several ways, but still enjoyed it. It seems as though at a high-level you're a bit railroaded into certain approaches, because many packages are terrible, and to avoid getting hard countered by certain bosses (such as Gutmook). Even so, it's still more flexible than arena deck-building.