How to approach fillets and/or how to fix naked edges

I need help on how to approach fillets and/or how to fix naked edges. The green shape is a solid I've created. I was able to put a small fillet (.3 or .2) on it , but there are naked edges. I've tried to fix the naked edges two different ways, but was defeated each time. I tied to detach the problem edges, untrim them and then match them. I get either weird joins or twists. (see blue ribbon shape) I ran a small pipe (.3) around the outside of the green solid and subtracted the pipe from the solid, exploded and then tried to use blend surface. I created several new surfaces. The purple solid looks like what I after, but after joining I have more naked edges than I started with.

Finally, I tried to redo my basic geometry to match tangency of curves at key points (I would prefer to be able to fix naked edges rather than let my ability to produce clean fillets dictate what shapes I can produce). The blue shape has curves that are tangent, but it won't take any fillet ( even .1 mm).

I know well your problem. However I did get yours to fillet. Well with a workaround anyway.
1. I used the sweep 2 rails.
2. I created the fillet profile at the 2 pointed ends on the shape
3. Then sweep 2 rails all the way around.

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