Thanks, Cheng, I didn't think about investigating children's hats.
I don't know what the story is with those hats... according to Turnbull, they were felt, maybe padded in the dome (my guess) but likely not.
I lived in Korea for a year during the 1990s. Those widebrimmed hats were a sort of fashion... from what I've seen in Korean museums and at recreated folkvillages, men wore a gauze, semi-transparent version of that hat, like an American cowboy hat, but flat-topped and flat-brimmed.
Other than keeping dust off the top-knot and signifying status, those hats wouldn't have been terribly pragmatic.
This costume prevailed into the early 1900s, so if you made Koreans like this, they'd still work with your 1700s-1800s Asian theme.
PS. Do you know who "Chinese Gordon" was? (The British engineer who took over Frederik Townsend Ward's Taiping-resistance army after Ward was killed).
I have a great idea for customizing him... will post if it works out...
-Tim