Any signs of molt on her anywhere? Any pinfeathers, check under wings and around vent, neck, head? They most often molt in late summer or fall, but some birds molt at other times, I used to have one that molted in April every year. Have you ever wormed her? I would crate her for a couple of days to see if she lays. If she is not laying, and possibly the soft eggs you've found could be her, or if she lays and you confirm the shell issue is hers, then I would give her calcium to see if it helps her pass anything. Calcium citrate +D is the best form, has better absorption, Citracal or generic equivalent, doesn't matter. Aim for about 600-800 mg once a day, for a week or two, or until she lays normally. It will help with contractions to pass anything, and if her calcium is low will help with shell quality. Just put it in her beak and push it back, she will swallow it. That particular dropping doesn't look terrible, but may have a bit of mucous in it. Hard to tell from one picture of one dropping. If there are other droppings that look different, please post pictures of those. Also check her crop. See if it's empty, full, hard, soft and squishy, etc. Check it again first thing in the morning, before she's had any food or water, it should be empty then.
@Eggcessive and I hit 'post' at the same time I think...
looks like we are both thinking along similar lines.