Sorry, but this completely misrepresents what LVT actually is, as well as suggesting considerably more agreement between Marx and e.g. Smith than they actually had; it's also wrong about the chronology of alternative theories, or at least the main one that came to dominate (and which is still considered mainstream).

Smith can be forgiven for giving an unsatisfactory answer to his own water-diamond paradox, as he preceded Marx by almost a century. But the originators of the formal theory of marginalism (Jevons, Menger and Walras — you likely know the first for his paradox) were roughly contemporary with Marx; they published their work only a few years after the first volume of Das Kapital, and well before Engels could publish the rest. The roots of the theory can be traced to Italian mercantilists contemporary with Smith, and even a bit further to Bernoulli (yes, the mathematician, the actually-turns-out-to-be-wrong explanation of wing lift guy).

https://en.wikipedia.org/wiki/Marginalism

More importantly, "believing that a carpenter banging wood and nails into a table creates value" is a strawman version of LVT that none of the people you mentioned would actually espouse, including Marx; and it is extremist, as it pays no heed to issues of either quality or utility, never mind market demand.