OK. I figured it out. Here's what I did.

1. After SWEEP, this small curve was generated at each corner. I then QUARTERED the model and threw away 3 of the quarters.
2. I constructed small lines to enclose the curve (co-planar to back surface) and then built out the long slim surfaces to boundary the pie shaped slice.
3. I then created the rest of the back using the straight lines from the slim surfaces. Joined everything and checked for 'leaks' (N key) and it was all good. So I mirrored and joined and voilà, a Solid!



File:
https://altuit.cloud/web/dbpub/3D/NextBook05.3dm