I just experimented a bit with Mike's approach. It seems like it might be possible. Here are the steps I did and an example file - I redrew your design as a nice clean extrude. I then added six of them together as a solid addition. I extracted the top surface of the stage. I tried decomposing this but VW wouldn't break it down. I then split the oval in half using a line and Clip Surface. I decomposed the resulting half oval. The resulting half oval had six polyline segments.
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