There is not just "a private conversation" but ample archival evidence for the Fed's concern with "Labor Militancy." You're right to ask the question of how this concern "evolved in time." For it doesn't even imply that "one of the most major concerns of the Fed was . . preventing economic conditions from becoming sufficiently good for Labor that they would be embolded to make strong demands on Industrialists and Rentiers:" Engineering recessions is a dangerous business that can only be justified, even in the most rarefied circles of the leading fractions of capital, under exceptional circumstances. Eccles' policies under Roosevelt's regime illustrates how, tactics must change with the changing dynamics of the class struggle. That is to say, it was fear of what I think you mean by "Labor Militancy" that prompted Roosevelt to turn to Eccles as his point man in the successful effort to break up the House of Morgan. After years of research that often boils down to day-by-day accounts of "the evolution of Fed Politics," I'm a bit reluctant to reach for easy generalizations that can be stated briefly. As Marx so eloquently shows, concepts must be carefully constructed to explain historical events that are not mere facts, unreflected and thinglike, but rather processes of infinite mediation. In this regard, I've never found the concept of rentiers useful in analysing the Fed's behavior. But in the spirit of the norms of internet discourse, I'll say that in the late-nineteenth century the Fed was a wet-dream of Eastern financial capital. The Fed only became a reality as part of the reorganization of the state apparatus in the wake of the concentration and centralization of industrial capital in the corporate form. Fed politics are most fruitfully understood, in my opinion, as a groping for coalitions and compromises to hold the original alliance together. Of particular importance is the struggle to find common ground between the large regional banks and the large New York banks. Sometimes the inter-capitalist rivalries become so intense that they forget that the whole edifice depends on the exploitation of labor, until some event forces the class struggle back to the forefront of their consciousness. Hope this is more or less what you were looking for.
Edwin (Tom) Dickens