I just read the intro to Francis Fukuyama's The End of History (yes, I will read the whole thing) and in it he says that the book is meant to be an argument for discussing history as coherent and directional, namely towards liberal democracy. He goes on to say that during the 20th century, the most profound thinkers rejected this view of history. He sees his book as restarting a conversation that was first taken up by Hegel and Marx, then later abandoned.
Fukuyama wrote that in 1992 and since then we've had books like Guns, Germs and Steel and Why the West Rules for Now, works that present a narrative of history moving in a particular direction and attempt to back up that narrative with scientific arguments (whether you think they achieved that or not).
The reason I was wondering if works like these existed in the 20th century is because there was an idea of history moving in a particular direction, at least in the popular imagination. I know academia in general had given up the idea, but was there anyone who tried to present a grand narrative? Or, if some idea of directional history existed, was it never presented with the same kind of academic arguments that you find in GGS or Why the West Rules?
The works of comparative historical sociologists utilizing a Marxist approach somewhat fit the description you provide - most are analyzing the mechanisms and social dynamics of political and social development, rather than making a political argument about the inevitability of certain outcomes as Marx himself did. However, since the works are often strongly rooted in Marxist theory, the use of Marxist class struggle arguments does provide a bit of a "grand narrative" structure.
Two major works of Comparative Historical Sociology from the time frame you reference: Theda Skocpol's States and Social Revolutions (1979) and Barrington Moore's Social Origins of Dictatorship and Democracy: Lord and Peasant in the Making of the Modern World (1966).
You might be interested in the works that came out of a perspective called World-systems theory. World-systems theory is an attempt to view the history of the world on a macro scale, seeking to understand wider trends at the level of the prevailing world economic system, rather than as interactions between nation-states. It has a long and complex historiography, and takes the Marxism of Hegel and, well, Marx as one antecedent, as well as various historians such as Fernand Braudel and Karl Polanyi.
The big names in World-systems theory include Immanuel Wallerstein, Janet Abu-Lughod, Andre Gunder Frank, and Giovanni Arrighi. I recommend Frank's RE-Orient as a good starting point.
Finally, a word of warning: Go ahead and read Fukuyama, but also know that his perspective is pretty outside the historical mainstream. It's an explicitly conservative perspective, a reaction to some of the destabilizing forces of the postmodern turn. While I think skepticism about postmodernism is a good idea, going back to a teleological view of history is not the best idea.