Grilling long beans, and a substitute for cooking twine
NO--I cannot emphasize this enough--you CANNOT use nylon rope (or any other random rope you have laying around, unless you can be guaranteed that it is 100% cotton or hemp)! It will melt all over your food. Cooking twine is generally, if memory serves, pure cotton and thus safe (though perhaps not tasty) to eat.

Tying your beans in bundles would be counterproductive; only the outer beans would cook. Unless you did some sort of weaving thing like a bamboo mat, at which point I would have to question whether the extra work actually saved you any time.

The mistake that most people make when grilling long skinny things is, as you say, to roll them. Or to flip them as though they were bigger objects. The trick is to turn them from their ends, so it's just a matter of grabbing the end--straight on, parallel to the bean--with your tongs, twist your wrist, move on to the next one.