Hi Mike,
I was going to send this to you and now seems like a good time (per our discussion at banquet). This may or may not work for you but I use it to touch up mine on the shaft (even though this is a carbon and un-screwable). Also this is a Centaur Big Game head but the concept is the same.
I cut a 8" PVC pipe in half and screwed it to a board. I then adhere wet/dry sandpaper to the curvature (radius) of the pipe by wetting it. I then pull or push my BH over the abrasive and fix the angle of the blade by only using my hands. It helps to blacken the existing bevel with a magic marker to evaluate your angle of engagement. Not precise but it does hone to a very nice edge when you acquire "the touch". I typically start with 400 grit and move to 600. Sometimes I finish with my paper wheel grinder and rouge. Note: no wet/dry paper on "jig" in photos. I also hold the BH when sharpening with both hands to establish the correct angle; my handhold in photos is for clarity.
Its not something one would likely carry in the field, obviously but you could certainly have it in camp.
For field touch-up, I use one of those very small, Mill Bastard, triangular files. Using the narrow tip, I file as I would any other BH.
Food for thought perhaps. Not perfect but another tick for your bag.
Kris