I’ve spent enough time in sunny villas in Tuscany to get a sense of it. Anyways, how did the cable break? If you can run a braided steel cable through some hooks or clamps it’ll be rugged enough to hold in place, I worry about the stone being too soft and tearing out from a masonry screw under tension, but it’s a thought.
Just saw your lattice comment, the lattice would be fine without being under pressure from the wysteria, as an additional sightline blocker but those sheets get hot and soften in the sun.