You can access Duelyst's draft mode after a certain number of ranked matches (I think it's 20, but it's been a while). The community on that mode is pretty small and dedicated though, so be prepared for a brick wall built from the people who've been playing it for eight hours a day for a year.
As a huge Duelyst fan, seeing the name turn up in my podcast app was super exciting, and it was really interesting hearing from people who aren't that into netdecks and watching the meta to climb the ladder, because that's where I'm hitting the game from. I'll stop myself from going through every query you had during the episode, but there are a couple of things I want to mention.
Firstly, you said you came around to the minion fight thing, but I still think you're underselling the extent to which the board gives you more things to think about. When there's such a mix of instant value and longer term effects, protecting the right things is a big question - I know Magmar could throw out a 4 damage AoE at 6 mana, what do I protect and how do I do that effectively? The act of committing your general is another big one - such a big token, even before you've buffed, is way too powerful to keep off the board, and it's a very delicate balancing act on working out when you need to hang around and when you need to back off for safety, as well as planning how to do that. The extra Chess flavour of maintaining safe yet threatening positions is what elevates it so far above it's competitor card games in my view.
I've also got a question: am I correct in inferring that Hearthstone neutrals aren't that important? Because there's no question you should be putting neutrals in your Duelyst decks. No faction has enough good 1/2-mana minions to get a full set of opening options, and neutral has some of the best stat lines and effects there are. Likewise, for some factions, the best removal is actually just to put in some cheap neutral dispel. There's neutral cards I'll put in every single deck I make except weird gimmick decks, which are never as good as more standard ones.
I guess what I'm saying is that I'm really happy this was a positive episode