This is basically it. "Capital stock" in a production context means a jumble of machinery that needs to be put into a certain shape in order to be productive. The discipline for that is called machine scheduling. That's combinatorial optimization. That's operations research. 
In order to translate "capital" from the production domain ("capital stock") to the finance domain ("capital structure") you need a transformation from the physical object to a fair expression of the value of the physical object. The name of that transformation is accounting.
So there is basically nothing that needs to be resolved. This is undergrad knowledge for anyone who has ever taken business and economics or operations research and economics together. The only way this could create any confusion is if your knowledge is so compartmentalized...
...that you know one side intimately but absolutely nothing about the other side and you cannot stop babbling because for some reason you think you know "production" from an economics textbook means you know production.
Absolutely nothing in an economics textbook chapter about "production" tells you anything about production. Production is operations research.
So that's the Cambridge Capital Controversy resolved. The End.
So that's the Cambridge Capital Controversy resolved. The End.
