Update time. I had some time on vacation to think about this little problem, and during that time I remembered something about a drill press mounted planer. Specifically this thing:
So despite the trade mashup, I ordered one. While I was waiting, I came up with a jig to hold the neck the way I wanted:
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The vice ensures that the work is parallel to the cutter, and the elastic arrangement at the headstock end allows tilt adjustment.
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The arrangement actually worked!
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I started out making quite large cuts, but then settled down to very fine increments. I did this by leaving the drill press table where it was and adding old business cards under the neck to bring it up a c*nt hair or two. I stopped early to give myself some breathing room; the result is very very nice:
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Onward!