I go nuts for the parallels between them; there's certain niavety and innocence to both of them, which is cruelly stripped from them, they both grow up believing in the archetypes of true-hearted maidens and knights, and dammit, they're going to live by those principals even if they're the only people in Westeros who are.

I completely agree with this assessment. Brienne is who Sansa would be if she were six foot four and could wield a two-handed sword. I do hope the two of them get to meet in canon. They should really BBFs.

...but if Jaime offered (any knight can make a knight, after all) she'd refuse because she'd think he was mocking her, even though he probably wouldn't be.

;_;

I'm also hoping that we might get a canon scene where Jaime actually offers to knight her. It would fit their thematic arcs very neatly.