Ynnek,
If the container shape changes, so does the shape of the rotational flights that turn it about. That would suggest that you would need a (matched pair) of fairly expensive rotational flights for every size/shape combination being handled. As an exercise in mapping geometry it would be a fairly interesting challenge (one I do not have time to undertake unless you are willing to pay for my time). Essentially you would need to map the presented shape of the container at (say) each 5° of rotation of the screw system and then loft cut to "stitch together" the shapes as they progress helically down the screw -- a seriously non-trivial exercise.
As a design engineer who has to compete on price and schedule for each project, I would use an escapement feed mechanism on a powered conveyor with a set of matched, shaped rotating wheels to catch the package and turn it in (say) 45° increments until I had my 180° package rotation. That way the changeover from one package size/shape to another is fairly simple and inexpensive. Adjust the (nominally) fixed width side guide rails on the straight feed sections, adjust the position of the escapement stop(s), and replace one set of turn-about wheels with another on the stepper or servo motors and be ready to rock & roll. ???