I received an email suggesting I use a hook to pull a strip of fabric through the layers to add heft for the grommets. Why didn't I think of that? I have a tool for turning sewn tubes of fabric right side out that worked perfectly for this job too. First, I cut a bias strip of coutil, which is sort of the twill tape suggestion on steroids, and pressed it along the center back curve to help guide it to the correct shape.
You can see I doubled the coutil. That may be overkill, but I figured two layers of coutil couldn't hurt since the linen is so light. I hooked one end of the strip on the tool and pulled it through. The pull ring was just small enough to fit between the stitching already done on the back panel.
The groove at the edge of the coutil is where I'll stitch the other channel. Grommets this weekend? I think yes.