This is very very crude. It's something off the top of my head scribbled on a scrap of paper as an outline for a first draft. But I will never go beyond that outline, because I wouldn't be any good at doing it.
The history of the Old Keynesian model is very quick. You have Keynes' 1936 General Theory, and Hicks' 1937 ISLM model. Done. All else is commentary.
The history of the New Keynesian model is very slow. It took about three decades. We need to divide it into stages.
(Or is my perspective biased by the fact that I wasn't alive in the 1930's and 1940's, and only started paying attention to economics in the 1970's?)
Stage 0. Late 1960's. The Phelps volume, and Milton Friedman's paper (pdf), both thinking about the microfoundations of the Phillips Curve, the difference between actual and expected inflation, and the role of monetary policy. This was the ancestral homeland of both New Keynesian and New Classical macroeconomics, which could not be distinguished at this stage. (New Classical macroeconomics died out in the 1980's, or some would say morphed into Real Business Cycle Theory, but New Keynesian macroeconomics continued.)
Stage 1. Mid 1970's. Now we see the difference. A distinct New Keynesian approach emerges. New Keynesians assume that prices (and/or wages) are set in advance, at expected market-clearing levels, before the shocks are known. This means that monetary policy can respond to those shocks, and help prevent undesirable fluctuations in output and employment. Even under rational expectations. Even if the central bank has no informational advantage. Because the central bank can act on that information, while price-setters cannot change prices until later. But monetary policy is still neutral, in the sense that anticipated changes in the money supply (not in response to shocks) have no effect on output and employment.
At this stage, there was nothing new about the demand-side of the New Keynesian model. They simply took the Old Keynesian ISLM, or the Monetarist MV=PY, straight off the shelf.
Stage 2. Late 1980's. New Keynesians introduce monopolistic competition. This has two big advantages. First, you can now easily model price-setting firms as choosing a price to maximise profit. (You get big discontinuities for perfectly competitive firms, because if one firm sets a price just slightly above the other firms' prices it sells nothing, unless all other firms ration customers.) Second, because if a positive demand shock hits a perfectly competitive market, where prices are fixed at what was the expected market-clearing level, firms would ration sales, and you get a drop in output and employment, rather than a boom. And the world doesn't seem to look like that.
Stage 3. Early 2000's. New Keynesians introduce monetary policy without money. They become Neo-Wicksellians. This is the stage at which they create their own demand side to the model, rather than borrowing one off the shelf. The central bank sets a nominal rate of interest, in response to endogenous variables like inflation and output, and exogenous shocks. Households/firms make intertemporal consumption/investment choices given the central bank's interest rate policy and their expectations. There were two advantages to doing this. First, it let them model households' and firms' choices without needing to model the demand for money and the supply of money. Second, it made it easier to talk to central bankers who already thought of central banks as setting interest rates.
Which brings us to the End of History.
What about microfoundations? Well, it was an underlying theme, but there is nothing distinctively New Keynesian about that theme. The Old Keynesians were interested in microfoundations too. New Keynesians just went with the flow, trying to make the microfoundations consistent across the model, as opposed to a piecemeal equation-by-equation approach.
Likewise with rational expectations. New Keynesians just went with the flow. Having a role for monetary policy to respond to shocks despite having rational expectations made New Keynesian macroeconomics distinct from New Classical macroeconomics back in the 1970's. But if you take a modern New Keynesian model and replace rational expectations with something like adaptive learning, it's still a modern New Keynesian model.