Command Blend (surface) can help ...



1. Make profile S1, S2, D1 D2, move S2, D2 profile to H
2. Extrude profile for surface blend reference
3. Use command blend (you can delete profile circle's and please select only edges) for blending extruded profile, delete extruded surface's
4. Extrude edge's from inside surface option tapered, (see attached file, object 5)
5. Select new tapered surface's and outside surface, use Boolean --> Merge
6. Remove unwanted surface's and join other