The first Swedish translation commissioned by Gustav I was a straight translation of Martin Luther's German Bible. The ones before 1917 were minor spelling and grammar updates from previous versions, direct translations from older Swedish.

The last two translations by the government's Bible Commission, The Swedish Church Bible of 1917 and Bibel 2000, were based on original Hebrew, Aramaic and Greek texts, but also made effort to minimize changes in style from previous versions, so now I'm curious how Bibel 2000 would have looked in some timeline where an intermediate Swedish Bible would have been based on King James.

Would they have gone back to the phrasing in the original text or would they have said something like "debt and sin are the same word in the original, but in this passage it's clearly more about sin"?

The 1917 version was more cautious, but Bibel 2000 did make some controversial changes in accordance with the originals and updated theological, historical and literary understanding, so maybe they'd have rephrased it to debt. We'll never know. =)