The number of BlendCurves used is set by the "Samples" property (20, by default).
A blend curve uses a scale value at each of its extremities, to determine its shape.
In order to reduce computation time, these scale values are not computed for the 20 Sample curves.
Instead, they are computed for a lower number of "Scale Samples" (3, by default), and interpolated
But this default value of 3 is obviously too low. I will raise it to 6.
Part Thickness is a very sensible operation that can fail quite often.
I had success with the round cap, but not with the other one.