I hate having to undo work. But I realized that I need to reinforce the plain seams so they don't rip out under stress, and I that it should be done before the reeds go in. So I pulled out the reeds near the seams, pressed the seam allowances open, made thin bias tape, and am basting it along the seams.
Once it's all basted on I'll sew down each side and the tape will help take the stress of the seam. I love how when making corsets, and stays, things that at first appear decorative are really structural. Like thin ribbon along seams.