bunnycat, I do the same with mousselines. I wash as I do twills, very briefy roll in a fluffy towel, but versus twills, I then take them straight to my ironing board (covered with an old, thick, damask tablecloth), and iron them dry, while avoiding the hems. If areas I haven't gotten to start to dry and crinkle a bit, I spritz with water, and proceed. One has to work quickly, but I've found the spritz method works fine. Like twills, they're not "like new" after washing, but I don't mind the slight changes, as I prefer to care for them myself. One thing I've noticed is that, like the twills, the hems shrink a tad, so after ironing, I very gently pull all the sides a bit. Then I place the scarf on drying racks to allow the hems to fully dry.
Sadly, I can't comment on washing changeants as

, I don't have any yet! What's your experience with those?