I'm not sure what you mean by "bleed into the new wall" but a wall in front of another wall should display as intended: covering the back wall.
I assume you want the siding like a baseboard: only part of the wall covered.
You can try three other approaches:
1 - Use sideboards for the siding (it's what they are for, best approach)
1 - Use boxes for the siding
2 - Use levels to split the walls in a lower part and upper part. Texture the lower part for the siding and the upper part as a normal wall.