What I've been doing with my convex edged knives is really simple and inexpensive. Get a mouse pad, 600 grit wet/dry paper, 1500 to 2000 grit wet/dry paper. I double sticky taped the paper to the mouse pad's squishy side, and basically strop away! Returns edges back to screamin' sharp in no time. Just this past week, cut up a huge pile of cardboard with a convex edged Lamey bowie... only took a few passes on the 2000 grit to get back to super sharp.
I'm sure this system will work well for the GB. Just make sure you use wet/dry paper and NOT sandpaper for wood. Probably want to experiment with the grits though. The grits I mentioned work well for knives, don't know yet the combo for the GB.
Mongo