Given that the parts for this are meant to be 3D printed and thus the people who have this presumably already have a regular 3D printer, it probably makes more sense just to make a rotary table for your cartesian 3D printer.

Also given that objects on the rotary table can not overhang without causing interference with the vertical axis column, there's really no harm in adding another column and spanning the horizontal axis across, instead of cantilevering it. This will provide a substantial improvement in rigidity.