I know you have a dislike for the Sharpmaker, but this is where it really shines. Just grind the edge with a coarse stone at an angle lower than the desired Sharpmaker setting. It doesn't have to be precise, just less. For the 15 degree per side (backbevel) slots on the Sharpmaker, just use an angle between 10 and 14 degrees. For the 20 degree per side slots, use any angle lower than 20 degrees. Then, after the coarse stone, go to the Sharpmaker and follow the direction, but use only the flats of the triangles and don't let the tip slide off.
If you don't have a Sharpmaker, then after your coarse stone, raise the angle a few degrees. Again, exact angle is not that critical, just find one that's repeatable. Alternate strokes until you remove the burr, or get the edge you want if you don't have a burr. If you have a bench stone, raise one end of it a couple of inches off the table for the coarse sharpening, then raise it another half an inch and alternate strokes for the final edge. Hold the knife horizontal and sharpen against the angled stone. For 8 inch bench stones, raise one end about 3 inches for ~20 degree per side angles, then add 1/2 inch for your microbevel, which will be ~23 degrees per side. For 6 inch stones, raise it 2 inches, followed by 1/2 inch increase. Use a magic marker to color the edge and see where you're removing metal from the edge. After doing this for a while, and understanding what's happening, you can skip the raising of the stone part and just lay it flat. FYI, this also works with the Sharpmaker with the stones on the back or front in the bench stone slots.