I am interested in this too.
My cynical view is that often demands for statistics and "hard facts" is, as Flora says, just a way of getting us to scurry off and do some admin. It's a challenge intended to put you on the back foot; it reinforces exactly where our culture places the burden of proof.
My experience is that "hard facts", when they are forthcoming, will be waved away. They are treated as "aggressive" or "petty" and "no one has time to get bogged down in the detail". Someone started an argument with me (about a work issue) on a "rational" footing the other day, convinced he would win, and when his arguments started to founder against mine, laughed at me and said "you're like a lawyer" and walked off. I was discredited for being rational just as efficiently as I could have been, had I taken a different tack, for being irrational.
I am interested in this and I do see the positivist stuff from both sides. I get its value but I also worry that there is a huge weight of potentially aggregatable (?!) fact about actual time, money, labour, violence, disadvantage, that consolidates into a huge lump of numerical material FACT and you miss that when you listen to individual voices in a more fluid way. And when you start saying "we have to listen to individuals' experiences" (which you do) you are in danger of it just being seen as individuals, just nice interesting little collections of stories, rather than a massive quanitifiable injustice.
But just as all these epistemological approaches have value and different purposes, I am pretty much equally defeatist about any of them actually gaining any traction when no one wants to listen to us, or has to, and I think it is a mistake to lodge the fault with ourselves that maybe we are providing the material in the wrong format and if we were to get that right, everything would be ok.