So I made my very first laterally offset headstock this week. I had inlayed a center strip in the headstock overlay to compliment my color scheme and despite my best efforts the center of the strip skewed slightly during glue up. I ,of course, did not notice this until I was all done carving the head stock and slotting for the tuning machines. I was admiring my work and noticed that the headstock was crooked! At least I had not attached it to the guitar yet. My problem was that doing the inlay before gluing on the overlay makes gluing it straight and on center absolutely critical. A solution is to wait until the overlay is glued on and then complete any inlays. Hmmm..... I like doing work before attaching things to the guitar in case is mess up. I mess up a lot so this is wise. Still, if I mess up an overlay after it is glued on but before I shape the headstock it is pretty easy to start over with little fuss. I usually use a laminate trimmer to route a groove in the guitar back and the headstock overlay. This works but there is just not enough room to balance the trimmer on the completed headstock for routing. I pondered this as I began constructing a new neck and I came up with a hand plane to do the job. This plane cuts a 3/8 wide groove that in +-1.5mm deep. These dimensions are fixed. If I want a different groove size I have to make a new plane. These dimensions work for me and are what I usually do for both the headstock overlay and the back strip inlay so I built the plane to match.
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To make your own is a pretty simple affair. Irons for plow planes are available at Lee Valley and a plane can be constructed around them. I made my iron but that is hard to do if you are not familiar with heat treating.
This sort of plane is worthless without a guide as shown above. Having a good straight edge to guide the plane is critical. Also make sure that you start planing near the end of the groove and work back to the starting point. Working in small bites helps to cut a clean channel.