Finally got your idea on OP’s Dcap (finially figured out had to extend long edges of top cap over Dcap and then project onto top conic surface, then 2 rail top cap end curve along those, then trim that new surface to top edge of top conic, then delete conic and remake top conic with 2 rails) Yeah, and it shells nicely 
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Well done. Your modeling will take a big a step forward now. Here’s another way I deal with singularities. I use extract iso curves and projected curves to trim out the singularity with a four sided opening. Then patch in that hole with a surface from edge curves.
Great, that is cool.
In a pinch I would just create a small sphere at the singularity, trimmed the sphere out of the surface and then patched the surface hole somehow.
Now I have more and better ways, thanks!
