I tend to use a lot of “faux” turquoise in the form of magnesite, a common rock that is dyed to mimic other opaque, veined stones. I actually like the pattern in magnesite because it is very clean compared to some of the grittier turquoises. I imagine the less “clean” turquoises might be due to impure varieties or being artistically reconstituted. There are times when you want that slightly grittier turquoise look though and here’s a decent faux for it.
Since this recipe ends up with a straight up marbled appearance which may or may not be what you want, you could vary it by using a combination of the marbled turquoise and normal “faux” clay turquoise that is chopped and tossed with the coloured sand grit. That way you’d get a combination of veining and marbling to make a neat organic appearance.