"Pure organic greens however are rare"
Not necessarily, there are a lot of wild plants that would probably give up their dye without the use of inorganic mordants, yellows in particular, blackberries and elderberries can yield different colours, roots also yield colour. The mordant for woad is of course urine which leads one to speculate if it could have been used in other dyeing processes. I reckon prehistoric women would have experimented....