After considerable google searching, some promising information, which seems helpful in understanding the requirements, was located.

There is a free "Feedscrew Generator" for solidworks at mecad. The installer is an .exe, so without Solidworks, not much help, but
there are some tutorials.:
https://mecad.co.za/
https://mecad.co.za/feedscrew-add-update/
http://mecad.co.za/feedscrew-basics/
https://mecad.co.za/feedscrew-addin-part-2-different-profiles-ins-outs/

There is also a Feed Scroll Generator Addin for Autodesk Inventor, many videos, and 26 page tutorial.
The 26 page tutorial is downloadable as pdf.
http://www.ldcadsolutions.co.uk/feed-scroll-generator.html
https://www.youtube.com/watch?v=ih67Mme2CLs
https://www.youtube.com/watch?v=gO1uVZ_f978
I have not located the actual Addin, it must be commercial.

So the algorithm would be something like diamond cutting, using a cutting object, the bottle, which could be one of a number of various shapes.
The screw begins as a long horizontal cylinder.
The cutter, or bottle, intersects the cylinder at right angles at the starting (left) end, to some depth radius, and is Boolean subtracted.
Then the cylinder rotates delta_theta, the bottle moves to the right delta_distance, (which could be a variable distance) and the bottle rotates delta_psi, and is Boolean subtracted again. Repeat until right end is reached.
(Or some alternative continuous version of the above... lofting profiles?)

- Brian