You can control the strength of the Length goals as some function of distance from the sharp corners like this:
InflateEdge.gh (309.0 KB)
When you have a curved surface coming down to a sharp corner like this, it has to form a cone right at the corner, so the bending radius goes to zero, which physical materials don’t really like doing.
I do wonder as well if there might be a way to make this sort of shape with NURBS. It’s a tricky one, but maybe possible.