Hi Barry,
Karsten's Motor2 node should be a big help.
May I suggest forming the two screws and bottle in .3dm, a la crankshaft etc.
Also a chart of the "engineering" would be helpful.
Ratio of helix turns to bottle turns.

Bottle turns 90 degrees as helix turns 4 times 360 degrees.
So the master slider (or quartz clock/timer/oscillator node) would have to be divided by 16 to feed the rotation node controlling bottle rotation.
It may also have to be negated for CW vs CCW.
The master slider would also, via a math node, directly feed two rotation nodes, input x, one for each screw. (One signal negated for CW vs CCW.)
And adjust frames for the LH screw's rotation node, and for the bottles rotation node.

Bottle moves x units to the right, from x1 to x2.

Does the screw need a bit of groove at negative x axis bottle width?
Rotation ccw/cw etc for the 3 objects.

Due to current work load, there is not much time to play with MoI.
- Brian