First, thanks for the explanation, but i still dont know if you can put a texture under the gamescreen, because all your examples are over the gamescreen... scanlines, shadowmasks, basically the whole hlsl chain is on top of the gamescreen. There is no example of a texture that is under a screen and for my approach, i wouldnt need the blending modes.
Just in case if you wonder why i want a texture under the gamescreen: because if distortion fx like curvature, corners and/or integer scaling is used, i dont want a simple black background around it. With a underlying texture, the distortion fx would reveal that texture.