Lots of things could be going on here and without seeing the heads or knowing exactly what you're doing it's all just guess work.
Using the KME broadhead jig? How fine are you going with it? It's possible you're raising a burr or wire edge and not removing it, or you're sharpening it just fine.
If you're not removing the wire edge you'll be distorting and rolling it with the sticks and leather.
If the edge is coming off the KME nice and sharp with no wire edge I'd leave it at that. It's pretty easy to destroy an good edge with sticks if you're not careful. I hoping your leather is
untreated with a firm temper. If you have any abrasive compound on the leather and it's not firm, you
will round your edge over.
Here's a guide to honing and sharpening that describes things well, even if it is focused on woodworking tools.
http://www.antiquetools.com/sharp/index.html Shaving hair off your arm and shaving your face are two entirely different acts that require different levels of sharpness (and different bevel angles) I can shave arm hair with a file sharpened head, but there's no way that'll shave my face.