OK..
Attached below is a spreadsheet which will calculate the required (simple) barn door arm length.
It is assumed we are dealing with EQ2 motor, and the associated gear reduction between motor box and worm on EQ2 is 1:5 - however those parameters can be adjusted in the spreadsheet.
If the above assumptions are correct, with the screw pitch of 1.25mm (which is a standard M8 screw coarse pitch), and up-gearing 2:1 (additional gears you have to find somewhere, from old printer for example), the required arm length is 199mm.
Up-gearing would be possible to avoid if the crystal is replaced with 2x higher frequency, for example - but this is a job for someone who has some experience with soldering.
I hope this will be helpful for you
