I wanted to share some progress for anyone else who may be going through this struggle:
I have continued to have baby E weighed weekly, and he still is gaining a good amount of weight. In the mornings, I do side-lying nursing with him (a royal pain with a shield,) and when he's done eating, I remove the shield but leave him there for some skin-to-skin. A few times, I have woken up to him licking and sucking milk off my bare nipple, which is SO exciting, because it shows he is getting comfortable with them! We are still using the shield at every feeding, but the other day on a whim, I tried to latch him on the second breast without the shield during a feeding, and he did it! Not only that, but he stayed latched and finished the feeding that way! We have not managed that again since then but I am sure it'll happen again. My LC is having me pinch my nipple quite close to the tip to help him get on, since he refuses to open his mouth wide.
Overall, I am really encouraged by our small successes and so happy to have stubbornly persisted despite all the discouraging obstacles. I definitely urge anyone else stuck in the same spot to hang in there, find an awesome LC, and not forget the little things, like skin-to-skin and just enjoying the pleasure of nursing! Even if you do have to use a shield!