The way we do rotary 3D printing - by digitally unwrapping cylindrical parts - necessitates a single vertical seam in the part, which is not ideal in most cases.

For parts with radial symmetry, it is possible to randomize the start point within the H-Series controller. 

First, insert a call to a macro at each layer change - this is done within Simplify3D by adding 

M98 P"/macros/shift"

To the Layer Change Script in the "Scripts" tab of the process you will use:

Next, create the macro to perform the shift:

The contents of the macro file will depend on the radial symmetry of the part. For a part that is a uniform cylinder, each layer can start at any point without affecting the final part, so we can randomize the starting point over 360 degrees. We do this by changing the Y value of the WCS:

M400
G10 L2 P2 Y{(180-random(360))}
M400

Where P2 represents the G55 WCS position. P3 would represent G56, and so on.

If the part has periodic symmetry, then you will need to adjust the values in the brackets so only offset by the period amount. For example - 5 identical and evenly-spaced fins extending from a cylinder have a period of 360/5, or 72. This can be achieved with the following code:G10 P5 Y{45*(2-random(5))}

M400
G10 L2 P2 Y{144-(72*random(4))}
M400

The starting point will depend on where the first fin is locate.