I can't really figure out what's happening with your file. I made a sort of workaround by exploding each of the curves, but you get a lot of individual pipes that can't be joined. I think the main issue is how the curved surface creates intersection curves which have a very slight bend to them, so when the piping algorithm attempts to trim the corners of the pipes, it fails, resulting in the small extensions you see.

Hi.

If you don't feel uncomfortable with mesh output, then you can use another option.

There are some line thickening tools including this.