I have some input for you to help you. Also I wish you luck and for the best. I hope this works.
So some things to consider...
I would not hang vegetables on string IF ...
If you live in some place with LOTS of high wind gusts.
Also, if you are in an area with too much heat and low humidity...
Or if you can't regulate your watering well...
I'm not saying don't do this. It does work for some people. But it can be less suited to say... the desert southwest. Or an area where you can't have the watering keep up with the water loss.
If you do hang them, people try to be careful about not moving the vines, etc too much at once. They limit it too a small amount each day.
You can still use either twine or fishine line. But instead of just putting it there you create like a blanket between either twine or fishing line to go between the line and where its holding stuff up. And this can be any trash cardboard etc. Also some of this where the line cuts into the plant can be from wind too not just from the plant's weight. So yes you can reinforce it with bits of cardboard but you want to not have it too tight. I did this with sunflowers one year, and it worked pretty well to keep the line from cutting in.
You could try paracord and some other things also. They have imitation parachord at dollar stores. But its less length than the fishine line. I'd still cushion whatever you use with like a homemade cardboard sleeve anyway no matter which one you do.
From where I'm at, I use a different strategy than hanging the vegetable plants because I'm in a southwest climate where our humidity is so low the plants will bake if I don't have some kind of foliage shield going on. But some people do hanging vegetables where they have smaller yards and have to work with what they have where they wish they had a larger lot size.
Good luck to you.