That's really interesting - I've seen this method being used for families of spoken languages, but it's the first time I've seen it for signed ones. In special the position of the Italian SL in the family surprised me a fair bit, because it's usually lumped into the same family as the French SL; perhaps similarities are due to diffusion?
The text mentions that iconicity might trigger false positives, but it's worth noting that it can also trigger false negatives, as a change in the real world prompts its substitution, and this introduces noise into the method. A good albeit anecdotal example would be the sign for cellphone in Libras (Brazilian sign language); it's theoretically this sign, fairly iconic (someone picking their phone from the pocket and bringing it to the side of their face), but I've seen plenty deaf people using another sign - where the signaller brings the hand to the front of their face/neck, the palm turned to themself, and the fingers curved. As if holding a smartphone close to their face, so what prompted the replacement is fairly obvious. (Specially since smartphones are way more useful for deaf people than old style phones.) And, while the research sensibly focuses on words present in the Swadesh list, they might also be prone to this sort of replacement - and it makes really hard to get enough data to unambiguously assign a language to a family.
Thank you for sharing this link!