I swept the back profile to the outlet profile (I had to modify the outlet profile to get a good sweep) with the 2 bottom rails... Then I took the curve from that original little top cutout you had made, and used to to boolean away the top (as Michael had just showed you... You can extract the edge of that cutout piece and flatten it in the top view with the edit frame, then extend the ends to be beyong the new swept surface) Then I deleted the flat surface from the boolean difference and created 2 segments of that inner edge to run a blend command on.. So that top piece is G2 curvature.. I could do this with the bottom piece too, but left it as it was because you had drawn it that way and figured you might want it to be shaped like that..

If this is too hard to follow, I could do some screen grabs for you..