The prototype phase of the
knit cap is almost complete! I've ordered the yarn to start the real live thing. In the meantime, if anyone is interested I'm typing up a quick pattern for the cap.
I had worsted weight yarn with a gauge of about 5 stitches per inch.
I cast on 81 stitches and worked in k3 p1 for two inches.
Then I increased to k6 p1 for 5 inches.
From brim to decrease I had a 7 inches.
I worked this pattern inside out because I could not figure out how to increase on a purl stitch. If someone is more savvy, they could flip the knits and the purls. This inside out strategy also meant I wasn't purling much which might be appealing.
My 1st decrease row decreased to the original 81 sts. Then I knit a row.
I decreased some more so I got down to k1 and p1 and knit a row.
I kept decreasing taking care to preserve the line of knit on the other side of the cap and knitting a row in between decrease rows. Eventually I ran out of knit stitches. So at the end I was purling everything, again to preserve the knit line created by purling on the right side of the cap.
Once I decreased down to 5 stitches I closed the hat by pulling the yarn through the stitches and weaving in the end.

The brim is another story. I traced a brim from a regular baseball cap onto plastic canvas. I used 14 squares per inch. I'm not sure if the 10 squares per inch would've made a big difference. Let me just say that it was too big. I ended up with a duck-billed platypus converter as a hat. QUACK! Is that what the platypuses say?
The idea is to pick up stitches and knit up a brim cover that you fold in 1/2 over the plastic canvas. This all worked fine and well. It was the brim that wasn't happenin. I guess baseball caps serve different purposes than winter knit caps. Duh. At least now I can dress my kids up as duck billed platypuses for Halloween whenever these kids come to exist.
In the meantime I'm still working on a reasonable, fashionable brim, but I'm certainly optimistic. I could always wear the brimless hat as well.