@The:
Yeah. Big Mam, for sure, is modeled after a Baba Yaga, and the tree in her Jolly Roger more than likely helps to represent that. I do picture Big Mam have a DF to do with consumption though. Kinda-sorta like the powers of Gluttony from Full-Metal Alchemist. (I'm sure Oda could pull it off and make it interesting).
Gluttony's Powers (at least in the Manga and Brotherhood) are more like Blackbeard's than anything. He was a failed attempt to recreate the Gate of Truth, which essentially turned him into an endless storage closet.
She made some pretty strong hints in her chapter that her abilities have something to do with dissolving. She directly mentions her stomach acid, which is a little odd to converse about without being a dead giveaway.