I do it like Mike Stewart shows at the website (SEE: Baron 1999 post).
I have a mouse pad. On one of the long sides, I've taped 1000 wet/dry, a strip about 2-1/2" x 8". On the opposite long side, I've taped 1500 wet/dry. I keep a 2-1/2" strip of 2000 wet/dry for later use (final stropping). At the final stage, I tape it on top of the 1500 wet/dry.
Remember to sharpen a Barkie (or any convex) like you were stropping it. Mike Stewart shows you how in the pictorial instruction guide.
Strop the knife on your choice of sandpaper grits, basing your decision on how "dull" the blade is. Use light to moderate pressure. Make sure you have a sharp, crisp edge before movin gto the next higher grit level. Whatever your final grit is (say 1500 or 2000), make your stropping passes very light on the final stage.
Move to a leather strop. *light* passes on the strop at the same angle used to sharpen.
Don;t worry about the scratches you'll get on your nice BRKT blade. They're inevitable. The only way not to scratch your blade is to not sharpen it... at least, as far as I'm aware of. You'll get better and scratch it less with practice.
Scratches can be buffed out with black or green rouge on a leather strop. Just work and work and work the blade around in circles on the rouge-laden strop *before* you sharpen. Then go through your sharpening stages. If you try to buff out scratches after sharpening, you risk dulling the edge with the strop.
When you finish, your Barkie should be the sharpest knife you own. It may or may not "pop" hair (mine don;t), but it will pass all push-cut, arm hair shaving, and other sharpness test with ease. If it doesn't, you need to go back to the mousepad and keep trying...practicing.