Thanks for all the comments!
Garmenta and Kendra - thanks for the Gap suggestion. Marianna - the Natori bra also looks promising. I'll look into them.
Angie and Carissa - I got this bra at Nordstrom after getting a fitting there; they put me in a size 34C. I tried on several different styles but this was the only one I tried that didn't feel scratchy. I have been washing them in the gentle cycle, but maybe it is the end of this bra's life.
Carissa - thanks for the suggestions about tightening the straps and getting some felt. I like that idea.
Maya - thanks, maybe I need to get a better fitting. From your thread it sounds like Intimacy does a better job than Nordstrom, so perhaps I should try going there. Definitely my bra shifts despite having been professionally fitted, so maybe I'm still not in the right size.
I love the thought that better fit could help me with the lace/seams problem, but honestly I don't think it's going to happen. My skin is just weird. For example, I have to cut the tags out of the neck seams and side seams of my clothes, because having tags against my skin makes me start itching like crazy after a few minutes.