Jonah, a very good point about Hillary’s roots, below.
But I suppose I don’t completely agree with your point about social Darwinism—though given the expertise you’ve no doubt built up in writing your book I state my view with trepidation. There is of course an element of malicious fun in referring to the old progressives as social Darwinists, but there’s also truth in it. It’s certainly true the term was brought into wide use in America (only in the late 1940s, I believe, by Hofstadter in Social Darwinism in American Thought) in an effort to describe attitudes that idolized competition, which he took to be mostly capitalist attitudes. But social Darwinism has also been used to describe the applications of scientific (or really in most cases “scientific”) thinking to questions of population and race in ways that make a case for public policy grounded in a preference for the strong over the weak—be it the physically strong or the socially strong—but not necessarily for free competition as the organizing principle of society. This is closer to the original use of the term, in the late 19th century. This kind of social Darwinism draws more on Malthus (who preceded Darwin) and Galton than on Darwin himself, and it surely informed the early eugenicists, and many people who argued (on various sides of the politics of those days) about the strength of the species rather than the well-being of the individual. There were many important progressives in that category.
Your term (or I guess Eric Goldman’s term) “reform Darwinism” is very helpful in clarifying the distinctions between these two quite different approaches. The laissez-faire social Darwinists opposed social reform as pointless and counter-productive, arguing that the problem was inherent in those who are weak and so could not be fixed by progressive reforms. But I wonder if “reform Darwinism” would not describe a sub-category of the social Darwinists, rather than a view to be contrasted with social Darwinism. Both wanted to apply insights from what they (in some cases quite mistakenly) took to be the teachings of Darwinian theory to social policy.