It's not a problem to get them at all. I only have 5 anthologies, because I don't heavily use them, and I know exactly which ones they are. I'll do a writeup on em for you later. You are basically doing me a favour because now I have another reason to avoid the load of laundry I really don't want to do.
Edit: the bit about how sigil breaks the epubs is exactly the behaviour I got while trying to fix the book. I had chapters out of order, and content missing, which is consistent with what you said about flattening of the folders.