To be sure: unless you're working strictly with convex models, backface culling is not an alternative to depth-checking or painters algorithms. A polygon can face the camera and still be behind another polygon. In other words, you need to make sure not to draw polygons that are further away on top of closer polygons regardless of whether you use backface culling. Backface culling is just an optimization based on the assumption that the check whether a polygon is facing the camera or not is much faster than drawing it (which, given the simplicity of the check, is always almost true) and a significant amount of polygons is actually facing away from the camera (which is true for about half of all polygons assuming your models have backsides)
By the way, why a reverse painter's algorithm?
Perform your vertex projection before doing the clipping.