I've seen something similar before, and sometimes I think about doing it when I have no assistant :p
Vance, maybe that could be adapted for your hat!
All sorts of hat for that matter ;)
One problem though, bouncing light off an umbrella with a hotshoe flash is not gonna have too much reach. I tried bouncing off from a Metz 70MZ-5 and the end result wasn't that bright, albeit soft enough.