Hi BS,
I'm not sure how far back you've cut it, but in saying that I can't answer the question of how much sand you require as I don't know how uneven your surface is and how perfect you want to make it. The last thing you want is high spots as that's harder to work with later than low spots.
Low spots you can always fill while high spots have to be dug out or re-profiled using a modified mower like I've got. BTW don't ever worry about the thought of killing a regenerative type grass as no matter how deep you cut there will always be roots in the soil that will grow new grass.
Maybe best you take some good photos of what you have to work with and put them up here so we can give you a bit of a plan to work with.
Cheers,
BB.
