Assuming you are rendering Redshift, use a RS Tag on the splines and set the RS Curve to hair or cylinder. That will solve the line deformation problem with sweeps - no sweep needed.
The curl/twist problem happens when you displace a group of splines (or a cloner with splines)... displacement works iteratively so it tends to look pretty uniform. Use a Connect object on them, drop it in a group with the displacer.
(And you can do the fade with some opacity/ramp trickery, but it is more flexible to do it with a depth pass.)
