First let me congratulate you some truly beautiful pies. They are easily among the best homemade WFO pies I've ever seen. I would have no issue with the level of charring on the bottom. The top, and especially the bottom, have the look I would like to see. I think you are definitely on the right path - just fine tuning now.
When you say the dough "lacked structure," do you mean is was overly extensible? My dough is extremely extensible. Gravity itself is almost enough to do all the work. My gut feeling is that you are not overfermenting.
Caputo flour, correct? How long are you working it in the mixer? About the same as I described? The acids prodcued by the SD culture I use will tighten the dough a little, it may be that is the only difference. You might try letting it go a little longer in the mixer. How tight do you ball the dough? When making my balls, I fold the edges under and up into the middle of the ball, over and over, until they are very tight - any tighter and I'd tear the skin. A little flour on the top of the ball helps. Pinch them closed at the bottom leaving as little seam as possible. If that doesn't work, try giving it a couple (2) folds just before you ball it.
I think Scott is right that I let my balls rise up just a touch more than you did, but not much.
Keep on it. I think you are really close.