Now completed a run with every character once. Definitely still don't feel like I understand how the characters can play in general but I've at least found something that works for everyone. For Ironclad, as mentioned above I did a huge defence stack thing. For Silent, I had a rapid poison deck (adding about +5-6 poison to all at the start of each turn, and two "triple one targets poison" cards). For Defect, I managed to build a Frozen core, lots of 0 cost card Claw deck with a number of cards to draw up those 0 costs like Scrape and All For One, felt really effective. Even with Time Eater being the worst final boss for this deck, I still destroyed it fairly easily, and I think never fell more than 10 HP below max in act 3.
It feels to me like I've had the most success seeing what my first few cards are, and then basically just going "I want to build a deck around this particular strategy" and then focusing on stuff for that. When I've tried to instead flow a bit more naturally and just seen where the rewards lead, I've found that I don't usually end up leading into anything that works. Like, in this winning run I'd picked up an All For One (I think from transforming a card) and only had one 0 cost card, I think it was late in act 1 or even early act 2 I decided to just start focusing on 0 cost cards and seeing what happened. I'm sure with more experience I'll be able to play in a bit more of an open minded way, ready to adjust based on rewards and relics and stuff, but for now I'm finding that tricky. Maybe I should focus on a character at a time for a little bit to get used to what they can do.