Tom Conduit writes
As Rakesh points out, the criticism that this category of "productive" labor doesn't include all labor which has social value (housework, childrearing, etc.) is a criticism of capitalism, not of Marx.>>>
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I don't disagree with your main distinction between productive and other labor.
Regarding the reasoning in your last sentence above, in Captial Marx has a different theory of value than bourgeois politicaleconomy. The latter does not see labor as the only source of new value. Marx also holds that workers are not paid for the full value of what they produce, bourgeois politcal economy and the bourgeoisie notwithstanding to the contrary. So why can't I, as a Marxist, also disagree with the bourgeoisie on housework and childbearing and rearing ,and assert that this is unpaid value producing labor ? The commodity that childrearing and housework produce is the labor-power commodity, the one that is the source of all new value in production.