Cathar will no doubt be here soon to comment, but in the meantime, I think you are overestimating the amount of material you will be removing when you lap. If you're confident it is "flat" and there's no deep scratches, then just skip to the last lap stage, which I seem to recall Cathar recommending 600 grit paper and kerosene.
BTW: I think you mean "...to such fine...", and not "....to suck fine..."
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