Good on you!

The fur backing is very (as I understand it) authentic. To help the leather lay flat you should have wetted it down. Oil only goes so far with veg tan (which I'm assuming this was). Give it a good casing, then temporarily attach it to the back. After it dries, you can remove it, dye it, and then re-attach the flat leather.

It looks quite nice, and I love your shade of green. It certainly seems strong enough to defend against a hail of beenie babies.