>capital which would accumulate in the hands of the capital owning class until capital entirely replaced labour in production.
I'm not sure if this is what Marx was getting at, at least from my point of view. Marx of all people knew that labour would always be required to work machinery, however his point was that the tendency for the rate of profit to fall was a consequence of the diminishing need to extract surplus value, as all a machine does is transfer value, unlike labour power it does not create value. To a certain degree, machinery has indeed displaced labour, though of course those employees which remain are more productive because of it, though that doesn't mean that more surplus is being extracted, at least not necessarily.
I don't think Marx intended to say that all labour would be displaced, and indeed in the long run a capitalist is intelligent to know that nobody will be around to buy back the products that his machinery creates. In chapter 1 of Capital he writes:
The introduction of power-looms into England probably reduced by one-half the labour required to weave a given quantity of yarn into cloth. The hand-loom weavers, as a matter of fact, continued to require the same time as before; but for all that, the product of one hour of their labour represented after the change only half an hour’s social labour, and consequently fell to one-half its former value.
I don't think he meant to imply that the value would srink to exactly zero. And as my sibling commenter has mentioned, the machinery itself requires production, and the machinery's value, which it transfers, must be given to it by labour. Machinery alone does not eliminate the requirement for labour, as you have noted, but Marx's theory doesn't require that it does.