I've always been bothered that punctuation at the end of a sentence has to be condensed into one - the mathematician in me wants total symmetry.
And so, for example, your last sentence:
I said "She said that her candidate was the 'best' and that my candidate was the 'worst'."
Let's play with it a bit and directly quote the female, to give us:
I said, "She said, 'My candidate is the "best" and your candidate is the "worst"'."
And now, in Rabrrrrrr's preferred mathematically coherent system, it becomes:
I said, "She said, 'My candidate is the "best" and your candidate is the "worst".'.".
And to get even more convoluted, let's make the last thing a question:
Did Steve say, "Helen shouted, 'Ernie said, "Dave asked, 'Is my candidate the "best" and your candidate the "worst" (ALL THREE!)?'."!'?"
Which in Britain would be:
Did Steve say, "Helen shouted, 'Ernie said, "Dave asked, 'Is my candidate the "best" and your candidate the "worst" (ALL THREE!)'?".'!"?
Sadly, in "proper" grammar, it would end up as boring old:
Did Steve say, "Helen shouted, 'Ernie said, "Dave asked, 'Is my candidate the "best" and your candidate the "worst" (ALL THREE!)?'"'"