Help "squeezing" a surface with projected curves?

I’m looking for any advice on how to “Squeeze” a solid shape with a set of projected curves.

Below is the shape and curves that I have:

And here is an image of essentially what I’m hoping to achieve:

(hopefully this image gets the idea across)

This is essentially my first project using the software so there may be a simple enough solution that I’ve just not been able to work out, but any simplified explanations would be greatly appreciated.

Grasshopper file:
torus with netting help - (12.2 KB)

Rhino File:
Torus with netting help - Rhino.3dm (156.3 KB)

Squeeze Pattern (22.9 KB)