My dear mother in law gave me my husband's coat and hat from when he was 3 (think JFK, Jr. at his father's funeral) for Violet. It's a lovely grey, all wool coat and hat, and has been well preserved in the cedar chest but the smell of moth balls is pretty strong. She tried Dryell 2 times and left it hang outside in the wind for several hours.
I would put it in an tightly enclosed space (like a plastic tote box) with lots of crumpled newspapers and a large dish of baking soda.
Baking soda works for getting musty smells out of books, crumpled newspapers work for getting pickle smells out of jars. And a cedar chest (or cedar balls) might also help get the smell out. You could also try spritzing it with a disinfecting mix of water with a few drops of essential oils like lavender, eucalyptus, peppermint, or tea tree oil. Sort of like eco-friendly "febreeze."