Here is how I finished making the larger doll's "garden hat." I had made the framework using floral wire, and it seemed to work, so I continued from there. I cut a piece of stretchy, thin cotton larger than the "crown." Then, I pinned the edges of it around the crown circle, so there would be looseness in the middle. I figured, it has to be loose in the middle for the head to go there, right?
I sewed a piece of cotton seam binding tape around the pinned edges to bind them neatly, and tried it on the doll. It sat okay on her head.
Then I covered the whole thing in old lace netting, simply putting the frame on the netting and then wrapping the netting around to the top -- pinned it in many places. Then did a lot of hand-sewing to tack it together at the crown and around the rim, and secure down all the lace embroidery.
Simple. Ribbons flowers made it cute, I think.
and it makes a doll hat that Esmeralda will enjoy when she is done.