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you have good geometry
once you have to triangulate it
you have very many triangles, quadrangulate don't do what you want, delete each unneed edge is very very much time
this script do this for you
1.edge have two polygons that are planar,
2.normals of this two polygons are the same (they look in same direction)
3.edge does not a uv-border
this mean that this edge you may want to delete, and script select it
how work - put scripts in your scripts directory, select polygonal object and write
0.01 - precision of planarity.
script only select edges that you may delete after look on it.