Not exactly "household", but if you can get hold of a microscope stage mechanism, and drive it with a stepper, you could probably get sub-millimeter movement.
Very cool with the DIY nut.. two things come to mind. One is that you could probably well-oil the rod and then form the "nut" out of Hotmelt glue, doing essentially the same thing as HDPE (might even be HDPE for all I know) except not having to do all that clamping and such. Epoxy grabs pretty tight and is more brittle usually, but "pouring" hotmelt into an impromptu mold would be simple.
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