The next big leap forward was reading Jeff Varasano and learning the basics of hydration. Turns out I was in the 45-50% range. I just needed to get that into the 62% or 65% range or whatever he says. It's counterintuitive because it's so hard to knead at that hydration, but it cooks beautifully.
I've started doing a long, cold rise like he recommends. I don't know how much difference it makes. I can't really taste a difference. But I do appreciate the goal of avoiding big bubbles.
I'd love to play with different yeasts next, but I keep killing my starters. Jeff has some good thoughts on starters. I like his recommendation to buy a known starter rather than relying on whatever is in your environment. I like the focus on predictability and reproducibility. But I think most people do wild yeast with good results. I think the Tartine book is also a good resource for the starter (and for a lot of things).