How can I made 3D strokes look like they're disappearing into z space?

I'm doing a project in which I want to simulate depth by having effects that zip into z space, etc. Above, I have some tapered 3D strokes in which I animated the offset to have it disappear, as if into the distance. However, the ends of the strokes won't seem to taper off correctly. I've been playing with start and end size, as well as all the other parameters of 3D stroke. But I can't get it to work. Can anyone advise me on how to make the ends of the strokes look like they are disappearing?
Thank you!

