So my second step should be to multiply the color of the fog sprite by Alpha and FogAlpha, and then add blend that over the result of the first operation!
Additive blending the fog sprite after alpha blending the first image can't be the solution, because if the background pixels and the image pixels are both brighter than the fog, there's no way to alpha blend them together to get a result that's darker than the desired result.
I got my pen and paper out to try to figure out possible solutions, but man, you sure don't know how to ask for help.