Hi - just saw this. I'm into my second year of making sourdough bread at home. I have been humbled more times than I want to say, so take this with a grain of alkalinity seltzer. Still learning and re learning things I've learned, and I'm a complete novice/amateur/beginner, but getting more consistent results as time goes on. I think. Maybe.
i've encountered exactly what you're describing, mostly in whole grain but occasionally with white flours. I've tried adding yeast - self defeating and doesn't help much. Baking powder or soda, not great results. I've used carbonated water and it basically adds more air bubbles for the starter to bubble in but it won't contribute to the actual "rise". May add some flavor too though, which isn't bad
It starts with the Starter - I have to work with it until it's super active - that means the starter will increase noticeably as I feed it and wait - say within 8 hours a really active starter will increase 50% in size and ideally "double". When it's doing that, make your loaves as soon as possible, using the starter.
I use a "1,2,3" rule for mixing dough - 1 part starter, 2 parts water, 3 parts flour. No more than a teaspoon of salt although you don't have to add that. They say to use weight instead of measuring - I've done both, either, whatever. I may add more water as I go, or flour, but having a good amount of starter in to begin with helps it to rise. The resulting dough ball will hold it's shape without immediately sagging or falling.
If the starter was lively to begin with the proofing should see rising within 4- 6 hours, I'm ready at about 8, but can take longer.
I've gotten good results going right from that first proof to a quick shaping and then second proof of maybe 1-2 hours or so and then onto my pan. I put a small tray of water in the back of my oven, to moisturize the bake - supposedly that gives it the thin crunch crust which is what I want and it seems to work. Then I bake at 390 for about 30 minutes. I don't back at higher temps as my oven seems to run hotter over longer times and I've ended up with bricks at higher temps.
Here's a few rolls I got, below. They started as about half that size, and rose. I don't think I did a second proof with them, they ballooned right up. don't have a pic of the slice, but they were airy and "bubbly" inside.
Having said that, I too am a batch away from my next set of bricks. Its' an elusive sport, this. BUT MAN THEY TASTE GREAT WHEN I GET IT RIGHT.
Let us know how you do!