Good news on the duct work, Drew. And dang, your spread there is looking really nice! My thoughts on your question about the lip, and consider the source now.... I'd forget about the lip and get all that carpet out of there!
Now granted, I've got way too many projects to be vacuuming very often, my my experience with burning wood is that you are going to have a mess. Ashes, embers, little pin burns... It looks like you can lay tile very well; if I were you I'd tile the whole room!