Linear stage for 20 mm motor from aliexpress with 28 mm mount base that is on the same line as axis. Lead-screw is ACME 3 mm diameter, also from aliexpress. I found that this motor is somewhat weak, so you may want to try other options or lead-screws with smaller step.

Parametric FreeCAD model is attached to match device to your needs.

Parameters that can be adjusted from a spreadsheet:

1. Diameter of the rails
2. Fudge factor to match your printer
3. Motor mount base
4. Motor axis offset n) Many more

To change lead-screw you need to import or design a proper one and do cut from pusher block.

I was able to print all threads precise enough, so that no taps was needed.

As of material, PLA has too high friction against steel rods, so ABS might be better. Nylon is the best, but it is hard to glue parts together.