Thanks for the advice @Leathercraft Masterclass! I tested 0.6mm goat with this one: Imgur: The magic of the Internet. It's surprisingly forgiving and easy to work with!
I used it for everything except the outer layer, so I was worried about the lack of rigidity. However, based on a few days of use, it seems to work perfectly as a bi-fold without re-enforcement, but let's see how it holds up in the long run.
Edges are DIFFICULT, but I guess just a matter of practice, practice, practice.