As you say, every case is different. You seem a very scrupulous and fair person so I don't doubt your motives and this isn't meant to be a pot shot at you. But many people, actually men, let's be honest, simply walk away from a marriage and children. They shed the ‘burden' and responsibility for raising their children altogether. Or they pay, dutifully and reluctantly, while raising a second family.
I'm looking at this more from the point of the child, who may also feel part of the failure of the broken marriage. I think any language of burden and resentment around childcare payment, even if not directed at the child, is unhelpful to them. A test of that might be how your daughter might feel if she read this thread, or guessed its contents, particularly at an earlier age. Certainly I felt sensitive about this when younger, and actually both my parents made clear they resented a) being saddled with the upbringing of their children single-handed and b) bearing the cost of it. Both would like to have been unencumbered.
It's hard to disentangle the resentments and animosities after a fractious divorce. That's why I was suggesting it might be helpful to consider childcare support simply as that rather than, as you put it, a payment “to my ex-wife”. If she mismanaged those funds, that's on her. At least you have paid your due towards the childcare. And, after all, she was the one bringing up your children while you moved on with your life, so she may have had resentments of her own to deal with. Maybe just think of it as a contribution for your daughter, rightfully paid, rather than as a burden lifted.