You only need a lawspeaker when disputes involve a lot of notables who don't necessarily see each other much and who also have a lot to lose (and fight over) if the judgement doesn't go their way.
I don't think this is the case, they were an important part of the institution in all cases. Often the dispute would continue after court, or rather than going to court, but this applied to everyone.
Next step is to write the precedents down, which I expect happened at some point. That may be a fruitful area of inquiry for you. When did Scandinavians start writing precedents down and when did the state administration start assuming the powers of the thing? Somewhere in there is where you move from custom to law.
For most European countries it was as I mentioned here >>9 basically they codified the law, and ended custom when the kings converted to Christianity and with it gained literacy. This is the case for the English, for the Russians, in Sweden it was supposedly due to less direct Christian influences. I think the Germans too. For Iceland interestingly it happened when they were conquered by Norway. Denmark by contrast was apparently never Scandinavian.
I would say that when agents of the state assume exclusive authority to make the judgement and apply the punishment - confiscation, violence, whatever - then it's law. Any similar actions that don't rely on the state, and it is custom.
That's fine although keep in mind customary law has a definitive (even legal) definition and does exist but it doesn't help me find a sound basis for the law which was my original concern, something similar to what I found for morality.