Nice progress. Diamond shapes are ok if they only have 4 vertexes and are merely a distored quad. 

For dynamic cloth, using triangles within a quad structure is a good tactic. However, what makes this method really work well is if the triangles have the longest side (the division of the quad) randomly flipped to the other diagonal. There are some programmatic ways to do this in other applications that Carrara does not have. But this method is kind of a purist method, and while I think it has the best results, the results may not be worth the effort in Carrara. At least until Carrara gets dynamic cloth! :D