Disregarding the fact the Dorset are not the Inuit, and also disregarding the sheer improbability of the Dorset crossing so much open sea (even in the depths of winter, the sea ice won't reach that far), the Inuit and their predecessors were by and large a coastal culture. They relied on hunting marine mammals rather than going after game inland--this is why there are few inland Inuit cultures, and why the Athabaskans displaced Inuit-affiliated groups like the former residents of the Anchorage area.
You are right on the Dorset. It was the suggestion in the original thread, but I see now that we would need Thule getting there a bit ahead of OTL schedule. Their skill package and seafaring were far, far in excess of the Late Dorset. The Inuit were noted to do longer sea voyages now and then, during the little Ice Age they reached Scotland on a number of occasions (
A. Trynkina (2014), ‘Kayakers near Scotland’s Northern Shores at the Turn of the 17th -18th Centuries: Main Theories of Origin’, Archaeology, Ethnology & Anthropology of Eurasia, Vol.42)
And yes, while some evidence suggests that the Dorset are related to the Athabaskans (DNA I believe, but they could just as easily be another Yeniseian branch in the Americas), they also weren't Athabaskan in that the Dorset of Greenland were incredibly far removed from their distant Alaskan kin.
Last I read, the Dorset were genetically seriously bottlenecked to the point of a single mtDNA line. They seem to have been genetically isolated for several thousand years. They do not show any more relation to the Athabaskans than to other native American populations and seem to represent a small migration of their own, not being part of the three main ones.
Iceland is not as marginal as Greenland and even in Greenland the later Inuit population at most was 2-2.5 times the Norse one before the 20th century(and the Norse didn't even settle everything as they co-existed with the Dorset over the island), in no other place inhabited by the Inuits from Nunavut to Labrador do we see higher population figures over far larger regions.
They might be as competitive in colder regions insofar as fishing is concerned but the Norse still can fill pastoral and agricultural niches in the south and some of the hinterland.
There can be some room for individual Norse settlers, which is not the same as a Norse takeover. Also presumably the monks would have some sustenance strategies of their own.
If Dorset Iceland somehow reached 100k people it would have more people that Greenland, Labrador, Nord Quebec and Nunavut had together until the 20th century. That's just hard to believe.
100k seems extreme. The entirety of Newfoundland had 500 -1500 people at the time of Norse contact. Western Greenland in the depths of the little Ice Age were estimated at 10 000 -30 000 and the Norse never managed mor ethan 5 000 in the same area during a time when it had much better climate.
The south-western coast of Iceland has a climate hardly different from the Faroes or even most of Western and Northern Norway.
Insofar as the Saami are concerned the Norwegians certainly heavily outnumbered them in Trondheim county if not even in the modern Nordland county, places like Lofoten were continuously settled by Norse people and never even had had a local Saami majority as far as I know.
Not so, and I live here. Its been a bit more complicated here. The Norse survival strategy was hitting its limits, and settled areas would expand when the climate warmed. When it cooled, the Saami pastoral strategy was advantaged and Saami areas would expand. Sort of like a slow timeshare on the lands. The Saami who lived on the islands and coast were known as the "Sjøsame",
sea saami. They/we (that far back the ancestral lines almost certainly blend) were more settled than the pastoralists and more involved in trade. They spoke dialects of the north Saami language.
What didn't happen was the Norse invading and dominating the area. (More like an one-the-average slow population expansion over centuries up to the present day.) But even with them being on the trade routes to Russia and a short hop away, they were not that interesting. They were not empty lands, but poor ones for the Norse sustenance strategy and further north.
There was the occasional settler family squeezing into a likely-looking fjord if it was not settled. TTL Iceland would have had much the same pattern except being further away, and not on any trade routes. OTL Iceland was deforested in short order, after which it was obviously poorer land, treeless and open without wood for tools or ships.
They didn't ignore the Faroes, Hebrides, Orkney, Shetland for that matter, anything that wasn't under a strong state such as the post-Carolingian kingdoms saw some amounts of raids and settlement, even if it was less settling depopulated or thinly populated lands and more creating coastal strongholds in places such as Britanny and Ireland.
Many areas that were not under a strong state got mostly ignored. The aforementioned North of Norway, Kola and everything north of Ottar. Siberia, the White Sea. Newfoundland explicitly because while it was better land it had natives. The Faroes, Hebrides, Orkeny, Shetland etc were actually on the way to richer areas, and part of the Kingdom of the Isles.
Eventually the island would be conquered by an actual unified kingdom though, the Icelanders were able to coalesce under one decentralized entity for centuries but it's questionable if Dorset people could repeat the process(especially if one believes they would have lower populations)
It didn't OTL, so I doubt it was inevitable. It joined up with Norway by agreement (the Gissurarsáttmáli) in 1262. There has never been a suggestion TTL Iceland would remain independent up to the 20th century though, just that it would be of insufficient interest to the Norse to attract more than individual settlers. Nor were we speaking of a Inuit polity but a hybrid one. It is possible that some Norse settlers could add items to the climate coping package
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