Eskimo/Aleuts had to cross the American Arctic to Greenland and from there to Iceland-it's quite a ways away! I don't think you can get them to Greenland-but you could get an alt-Inuit culture developing natively in Greenland, perhaps? A Greenland or Eastern mainland Dorset culture rediscovers the bow, the drill, and builds umiaks before the people of the Aleutian Islands do, and so the *Inuit culture moves from east-west instead of west-east as per OTL. With a start closer to Iceland, they can manage to make contact there. It's not advancing the culture technologically, just having the advancement occur elsewhere than OTL.
I think that native inhabitants of southern Greenland would see off Norse settlement. The Norse might have iron, but they don't have numbers or a germ warfare advantage, and while they probably could conquer Greenland if they tried, the level of organization this would take and the lives lost for what is ultimately a frozen island is probably not going to be seen as worth it. Native inhabitants of Iceland would be in a somewhat tougher spot due to the fact that Iceland does not have large animals for them to hunt, but Iceland has very rich seas and with some management they could sustainably harvest resources like puffin eggs. We might see Norse explorers meet *Inuits in the process of conversion to Catholicism by Irish monks, who Norse legend claims had settled on Iceland. The Norse may conquer and dominate, but I think there initially would be room in Iceland for both *Inuits and Norse, with the Norse focusing on farming and the *Inuits fishing, sealing and hunting birds. As the Norse Christianize and the Little Ice Ages begin, farming becomes less useful and the cultures start to merge, with the Catholic Church providing the opportunity for peaceful intermediation between the two peoples. Modern Iceland looks less like an outpost of Europe ITTL and is the first Native American-European Metis culture instead, with the Icelanders themselves probably benefitting from a slightly less homogenous gene pool from their founding population.