Not exactly what you are looking for, but you may still want to take a look at Moore's /Foundations of Mechanical Accuracy/. IIRC, it contains a section on the evolution of machining since the early 1800s and covers the transition between the making of parts made to fit together, to parts made to specs.

BTW, in later parts of the book, Michelson appears as interferometry is used to check the accuracy of parts.