Even if you put the triangles off screen they are still rendered. If one part of a surfaces is showing, the whole surface is rendered. Either reuse the quads, OR, rebuild the surface from scratch.
As to ordering the quads, unless alpha is used, they are drawn in the order of distance. You could move the quads slightly forward. This however, will probably have a negative impact on the pixel perfect code.
As to ordering the quads, unless alpha is used, they are drawn in the order of distance. You could move the quads slightly forward. This however, will probably have a negative impact on the pixel perfect code.