Another method that can work is to draw a polyline with some points snapped on to your bendy curves, then sweep using that polyline, which will succeed since the juncture between every pair of lines is able to use a planar intersection to cut it, so it won't have any section/section intersection problems.

That will make a segmented result like this:



But then to make a smooth result from that you can select all the edge curves at the ends of each of those segment pieces, and use Ctrl+C / Ctrl +V to extract them as standalone curves and then loft some smooth surfaces through each section like this:



The attached 3DM file was done that way.

In the future I want to add a mode to Sweep that will do this kind of corner construction as well - it is not the exact same "rigid tube" type shape as the true linear extended and intersected type of thing that the corner mitering only tries to do currently though.

- Michael