Underpainting or grisaille

I have used Winsor and Newton Artisan water mixable oil colours of Burnt Umber and Coeruleum well, diluted with water, resulting in a transparent warm brown. Hopefully this will balance the high oil absorption of the paint which makes them unsuitable for under layers. Budget constraints means that I can not buy more paint. The canvas was covered in a layer of this paint and it was wiped from the areas that will be light. Then I painted the lights more opaquely using Titanium White, Burnt Umber, Coeruleum and a tiny bit of Indian Red. Elliott recommends using flake white but this colour is not in the Artisan range. The next step when the paint is dry is to paint transparent glazes for the shadows and dark areas.