I have done several feature rings, using this technique, and agonized for a long time about how to deal with the dramatic change in appearance as you turn away thickness. I eventually came up with a technique that completely eliminated the distortion on the vertical spacers, or vertical elements...or at least it works for me. I'll try to explain it...
I start by cutting all the pieces for assembling the feature from thin stock. The key to the technique is that all HORIZONTAL elements of the feature are cut to the shape of a segment...trapezoid shape with angles corresponding to the number of segments you have chosen. Then, all the VERTICAL elements of the feature are cut rectangular...no tapering at all...essentially serving as a vertical spacer. During assembly of all the little pieces, and glue up of each feature element, it is important to not sand very much...just enough to give a good glue surface, and not enough to change the taper of the horizontal element or to introduce a taper into the vertical elements.
Once assembled into a feature ring, you can turn away (from either the inside, or the outside) as much wood as you want. The vertical elements will never change thickness. It is only the horizontal elements of your feature that will change length as you turn away thickness.
Not sure if I explained it clearly enough, but in practice, the technique works very well for me.