Thanks for all your suggestions! Some progress update:

Wodka spray: Getting rid of quite a lot of smell
A night in the freezer: Not a lot of effect, some: not good for the pleats with it being folded.
Half an hour in cold water and letting it dry: no effect whatsoever
Baking soda in an airtight bag: this seems like a winner and has removed the smell from everywhere except the middle part on the inside where a lot of different fabrics meet.

I might have to try the woolite bath Plaid Preacher suggested earlier. I’ll put the cedar wood blocks closest to the smell overnight, we’ll see what that brings.