The King of Norway did not outright control Iceland or Greenland until 1255-1264.
Iceland did have Althing, which in 1000 made a decision to accept Christianity. Between, say, 1000 and 1024 - which enforcement activities did Althing undertake against remaining heathens?
In Greenland, Erik the Red was a heathen till his death in 1003 - his wife became Christian. Of his children, Leif was given the mission of converting Greenland to Christianity - but his sister Freydis stayed heathen.
Suppose that it is Freydis whose Vinland expedition goes better than OTL, with the result that a permanent settlement is founded.
Freydis had a husband, named Thorvard, but she managed to get him to do as she wanted.
So, say Freydis and Thorvard successfully found a settlement. She bears a son, named Snorri as per OTL, and after a few years, e. g. Thorvard dies leaving Freydis an unchallenged leader of the settlement (her brother Leif is far away in Greenland and it wasn´t him who made the Vinland settlement last, while her sons are a few years old). In Iceland, there were 13 first settlers who were women, out of 435 or so total. These included:
- Ljot who came from British Isles with her brethren Hildir and Hallgeirr; unlike most other sisters who came with their brethren and soon married and moved to husband´s settlement, Ljot founded her own Ljotarstadir
- Thorgerdr whose husband died at sea on the voyage to Iceland - the widow arrived with their sons and, since the sons were apparently young, it was Thorgerdr who was regarded as the settler
- Asgerdr Asksdottir - after her husband was killed in Norway, took their children (again presumably young) and also her half-brother to Iceland, and seems to have been treated as the guardian of her brother
- Audr, who moved to Iceland with a bunch of granddaughters after her husband and her son the father of the granddaughters had both been killed. She was a Christian all her life, but after her death, her descendants converted to paganism.
What were the names and stories of the other 9?
So suppose Freydis Eiriksdotter is the leader of a successful colony (her husband having had less influential relatives and being dead, her sons being small). And even when her sons come of age, she keeps her entrenched leadership position till she dies of old age. She also is openly heathen, and while she may not outright persecute Christianity (too much bad relationships with her brother Leif and later her nephew Thorkell), she does favour the settlers who are heathens and felt uncomfortable in increasingly Christian Iceland and Greenland.
What next? When Snorri Freydisson (sure, the name of Thorvard is remembered, but Freydis is the leader who is important... King of Denmark Svend also stuck with the name of his mother Estrid Svendsdatter and not of his father Ulf) finally inherits in his middle age, say 1050s, what is the heathen/Christian ratio in Vinland? And what will Snorri do?