A couple bits of experience:

- Sour flavor and bread with a lot of rise are mutually exclusive. The very same thing that gives you sour goodness (lactobacilli doing their thing) also gives you acid (lactic acid), which nukes the gluten you need to otherwise have bread with lots of air in it.

- You can cheat and use chemical souring agents ("souring salts" in the King Arthur catalog). Don't do that.

- You can keep your sourdough starter at a lower hydration. I keep mine at 50% (i.e., one ounce water to two ounces flour). This seems to help a bit.

- You can adopt a binary method, where you make two balls of dough. One of them has flour, salt, water, nothing else (a "soaker"). The other one has sourdough starter, flour, water (a "preferment" or "poolish", among other synonyms). You let these go for a day or more, combine, wait a few hours for the sourdough to rise things, and straight into the oven. (Greater than a day, put the soaker in the fridge so it doesn't start fermenting on its own.) If you're doing a mixed grain bread (e.g., part rye, part white), then do the soaker with the white flour and the preferment with everything else. Thus, you're building up sour goodness and acids where they won't nuke all the lovely gluten.