"The plot thickens. I made a similar object but much simpler with only 14 holes. The unsmoothed mesh was 180 polygons and in Vue was also 180.
After smoothing the mesh was 720 polygons but in Vue was 960.
After smoothing again it was 2880 polygons but in Vue was 4320.
I can't see any logical reason for this."

I'm guessing Vue is probably triangulating all polys greater than 3 sides, as it does when importing objects, as triangles are guaranteed to be coplanar. And since it appears there are a number of concave polys, it is taking it's time.