I finally tried Liz Clark's Slatted Sunbonnet Pattern. It's a very simple pattern (and authentic), but does have a lot of stitching (for all those slats and a very big hem). Of course I also had to cheat (don't know why I can't follow instructions) and I did just put heavy interfacing in the brim area rather than actual slats. I cut my interfacing big enough to cover the space that slats would cover, then just stitched lines over the interfacing. I can still put slats in, too, if I want to make it stiffer.
You'll be proud of me, though; I did hand stitch my hem! Can you believe it? Me, the anti-hand-stitcher. The hem is curvy enough that it would have been a pain to machine sew.
The nice thing about this bonnet is that it is adjustable because of the ties inside and outside. You can make the brim go out as far in front of your face as you want (see images).
This probably took me around 2 hours.
I'm now working on, yes, another bonnet. I don't know where the pattern originated, so I don't know that I'll be able to post the pattern, but I'll see what I can do.