Inuit made it quite far afield during the little ice age. They could reach Iceland, and get back there even. The problem is competition.
They couldn't hold off the norse outside of their environment. Speeding up Inuit expansion just means the vikings slaughter them on Iceland.
What is needed is some way of cutting off the Norse expansion. Something bad happening in Norway/Denmark. Perhaps combined with earlier Inuit expansion.
Maybe a severe volcanic eruption, or several. Weather cools. Scandinavia does not produce a population surplus. Meanwhile, the Inuit spread faster due to less competition from the Indians, whose strategies were not as well suited for a cold spell as the Inuit.
Iceland is settled by the Inuit, at abut the same time as the Irish monks. For once, two cultures with no cultural imperative to conquer their neighbours meet, in a marginal environment.
The monks convert the Inuit to the Celtic Chruch, the Inuit provide the bulk of the population base, and an exceptional set of survival skills. Cattle and corn only become supplements to the diet.
A vibrant hybrid culture results, with much classical learning being preserved by the church in the more peaceful and remote land of fire and ice.