So I browsed through the hat's gallery of finished projects until I found one by Sal, who had worked the hat band as a headband, just the way I had pictured it! :-) Sal said all it takes is to work an i-cord bindoff to make the top edge of the headband look like the bottom edge.
Following the hat pattern's directions, work through the part where you pickup the stitches at the top of the band. Then, instead of knitting a crown for a hat, work an i-cord bindoff. To invisibly join the ends of the i-cord bindoff, see this video.
