I agree, a twining vine that goes around a thin pole or string might have trouble getting through the holes in your mesh, Dinu. If you checked every day, and 'helped' the tips to thread into the holes it would work, but . . . that's somewhat tedious. Clasping vines like passiflora or the Gloriosa lily would do great with that mesh.
I'm thinking in India, so close to the Equator you don't have much of a dormant season, so cleaning off the dead foliage may not be an issue, yes?
I had that same experience with the black garden snakes here, June! I had to stop using bird nettting on my fruit trees because these crazy snakes climb up the trees to ambush birds and rodents, and would get caught exactly as you describe. I managed to free two of them - a hair-raising exercise although they are not venomous, they do try to bite you - but a third died before I found him.