Thanks for the suggestion. Unfortunately, that doesn't solve my problem. First, I need miter gears, not spur gears. But, McMaster also has imperial miter gears in nylon.
Adapting from 6mm to 1/4" is actually very hard, unless you have lots of axial space for a coupling, because there's not enough space for a sleeve type adapter. Just screwing them on a 6mm shaft leaves a 0.35mm difference in concentricity, which is quite significant and jams up the meshing.