[Mike Everman]

I of course love the screw rack idea. I say of course because I've put some effort into it in the last few years, off and on.
Making pinions out of steel was not particularly difficult when you make a simple tool.
Blanks are put in this fixture and a spiral flute tap used to make two at a time. It is not as perfect as hobbing, where the ratio of tap rotation to pinion rotation would be tightly controlled, but it works well. Plastic would be doable with a hand drill and just two pins in a plate at the right center distance.

You just need to calculate the pitch diameters of screw and pinion, such that the pinion pitch is an even number of teeth (obvious, I know, but if side cutting just one you can feed toward the center until you find a spot where the teeth look good; in this case I've nailed the center distance, and machine two at a time so there is no side load on the tap.)