So the kisses could be returning some of Jareth's power to him or granting Sarah whatever she needs to complete her tasks?

Oh, I like that idea.

The verse of Threes talks about kindness, honesty and faithfulness so at least one of Jareth's three things (vows, sorrows, truths) might be related to those?
Well, yes, they are exactly related: kindness <-> sorrows, honesty <-> truths, faithfulness <-> vows. Just like in the Sevens verse, kisses <-> love, and riddles <-> wisdom.

I sort of like the idea that healing sorrows is somehow related to helping the inhabitants of the Labyrinth. Jareth has always been rather disdainful of them and the curse does seem to be aimed at encouraging him to mend his ways.
(nods) I wonder what there is in the Labyrinth to be healed?

Or history because she loves the stories behind the facts?
Ah, now I like that idea. Particularly since part of her motivation could also be to leave behind her childish fancies.