I skipped that plywood/tube -combination, and made it altogether a little more solid component:

Original plan was to make this jig for small (3mm(~0.11") and below) drills, but the chuck is bigger, and so will be the whole device.

To add even more confusion, I intend to use a small(dia. 13mm(~0.51")), slowly rotating(~100-200 rpm), diamond coated grinding drum for sharpening:

Ordinary grinding wheel would wear on such a low speed. Instead, the thing above seems to last. I have used (and abused) that thing with glass, plastic, wood, HSS, carbide, and various other metals.
Anyway, the jig itself needs still some work to get it ready for testing

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