I’ve made a little progress on this now.
I can run a menu operation on a mesh in Unity, and it will reconstruct the mesh from the Collada DAE file keeping all of the information I need that Unity discards during triangulation:
It’s early days, but what I’ve got here is the re-constructed mesh, and spheres that are sitting in the middle of the original quad mesh faces.
And a blue sphere that is sadly not where it should be.
One of the main reasons for me making this quick post, though, was that I failed to reference a really awesome blog post by Rory Driscoll about this subject from about 5 years ago that will make my life very very easy!
http://www.rorydriscoll.com/2008/08/01/catmull-clark-subdivision-the-basics/