Just an update: I restarted the chapter on Intermediate to help me get past Velvet and the hat drops from the painting now. It must have been some issue with the patch coming out while I was still in Reine.
Here's a link to the video:
I don't know if the order of the hats matter, but I think I had them collected 1, 3-5, 7. I tried to get #6, but it didn't work. I finally got #2, but #6 is still doesn't drop.
I think I've talked to all the NPCs and the pictures around Reine.