You made it sound like "strong viking win raaagh", which it was not, but hey.

It was a democracy, and of course a democracy elects someone with a certain amount of prestige and so on. It even builds up to specific clans/dynasties without intervention against it (equalizing wealth). I think the new republic system should function rather well for this, except that pagans should be able to hold castles independently of the cities that are tied to the top republic title, in order to represent the land that these families held independently of kingship for example.
An example: The king of Denmark has 3 cities and 4 castles. Upon his death the 3 cities will pass to the one who is elected king and the 4 castles will pass to the next head of his dynasty. Every title would function like this for the Norse. So if a Lord Mayor (Hövding) of Sjælland dies while having 2 cities and 2 castles and the successor to the county is not of his dynasty (due to republic election) his two cities would pass to the new Lord Mayor and his castles to the successor of his dynasty (who would now be a baron).
That is how I would picture the Norse functioning properly. I really want the feudalism and the democracy blurred into each other.