By complete you mean the healthiest and least at-risk of going extinct? Of the languages on the map, these would be Cuban Sign Language, Honduran Sign Language, Guatemalan Sign Language, and Nicaraguan Sign Language. These are not Indigenous languages so it’s a bit of a boring answer.

Greenlandic Sign Language, despite being a national sign language, is in a bit of a different position. DeafNation says that there are only 10 Deaf people in Nuuk; SAGE Deaf Studies Encyclopedia says that there are 20~30 Deaf signers in all of Greenland; and peoplegroups.org, a sketchy missionary website, claims that there are 325 d/Deaf people in Greenland total. I suspect that DeafNation’s number is actually counting the number of Deaf signers in Nuuk, so these numbers then suggest that fewer than one in ten d/Deaf Greenlanders know sign language. This fits with what’s known about Greenland’s Deaf education: the country’s only Deaf school is a primary school in Sisimiut, and the country is otherwise on the whole extremely pro mainstreaming and not very accommodating of sign language at all. Migration might be another factor: I don’t exactly have statistics about this, but it wouldn’t surprise me if Deaf people in Greenland’s villages moved to Nuuk at greater rates than their hearing peers, and in turn if Deaf Nuummiut had a greater rate of moving to metropolitan Denmark than their hearing peers. So Greenlandic Sign Language to me seems like it could be displaced by Danish Sign Language, if it isn’t just Danish Sign Language already — extremely little has been written about Greenlandic Sign Language.

Nunavut has supported Inuit Sign Language (IUR) a lot more than Greenland has supported Greenlandic Sign Language: meetings of the legislative assembly are simultaneously interpreted in ASL and IUR, and a bunch of resources were poured into documenting the language and creating learning resources for it so that Deaf Nunavummiut can, if they so choose, pursue an education in IUR. However, by the time IUR was even recognized as a separate language, ASL had become the sign language of more than two-thirds of Nunavut’s 150-ish-person-strong signing Deaf community thanks to the boarding schools. So, it seems likely that Inuit Sign Language will continue to be increasingly displaced by ASL.

The easiest languages to describe as extinct or on death’s door are Old Cayman Sign Language (might already be extinct), Plateau Sign Language (extinct, but a few people remember a few signs), Martha’s Vineyard / Henniker / Sandy River Valley SLs (LONG gone!), and Old Boricua Sign Language (presumably extinct if it ever existed; as said, I can’t find anything about a language by that name online). Sawmill Sign Language seems like it might actually be referring to Expanded Oregon Sawmill Sign Language, a language that apparently emerged in the 1950s when a late-Deafened retired sawmill worker used a blend of rudimentary ASL and the pidgin sign language of his former workplace to communicate with his wife and also-Deaf son. The son might still be alive, albeit very old; the parents are almost definitely dead by now; the son probably didn’t teach his own kids the language. So this language might also already be extinct, though Sawmill Sign Language in general might still have a number of people who remember it, even if they’re all retired and no modern sawmills use it.

Maritime Sign Language and Jamaican Country Sign Language (KS) are also both mainly restricted to the elderly now. KS, however, in 2009~2011 had way more speakers than MSL (7,500 vs 90) and a lot more resources being put into documenting it. MSL had a lot more historical institutional support, but that doesn’t seem to translate to much now that there’s <100 speakers left. There’s still some work being done to document MSL, but not nearly as much as with Jamaican Country Sign Language.

As for the remaining village sign languages of Provisle, Mayan Sign Language, Albarradas Sign Language, San Juan Quiahije Chatino Sign Language, Orocovis Sign Language, Keresign, and Navajo Family Sign… I’d describe village sign languages as the Riftia (giant tube worms) of language. Riftia colonies can thrive and be stable at the right thermal vent, but the thermal vents are themselves an unstable environment. Which is to say that village sign languages emerge when a village has an unusually high rate of congenital or early-childhood deafness, so as long as that unusually high rate of deafness is there, then the villagers will continue to have a reason to learn how to sign; but the moment the rate of deafness in the village drops to the same levels as the surrounding villages, then like a thermal vent dying, the whole ecosystem collapses, and it becomes very easy for the village sign language to be displaced by the dominant sign language of the region practically overnight — well, as if these languages aren’t already being outcompeted.

Then there’s just Plains Indian Sign Language and Oneida Sign Language to talk about. Truth be told, I can’t really say much about these. Efforts to document PISL started a lot earlier than efforts to document many other sign languages, and to this day I get the impression that there are a lot of resources being put into documenting PISL; nevertheless like all Indigenous sign languages, it faces the double marginalization of being Indigenous and being a sign language, and this has made it very difficult to transfer PISL between generations: it lacks both institutional support and a “thermal vent”, so it’s mostly relegated to elders now. At the same time, I recall reading a story (which I’m struggling to find now) of a non-Indigenous late-Deafened person who voluntarily chose to learn PISL instead of ASL because they just found PISL easier. This seems like sort of a fluke, but it still makes me hopeful.

Oneida Sign Language is, as said, a modern revival language, and it’s currently largely relegated to a small number of elders, but I don’t know enough to say what its trajectory is.