Chris Dillow, information equilibrium is the framework you're looking for

I think Chris Dillow makes a fine point at the end of his review of The Econocracy about the role of the media with regard to how macroeconomics is disseminated and perceived. I just wanted to add a bit to something he said earlier in his post regarding teaching economics:

For example, some important basic facts in macroeconomics are that: there’s no such thing as a “representative firm” (see this great paper (pdf) by Nick Bloom and colleagues); that GDP growth in developed nations is often stable but interrupted by occasional crises; and that recessions are unpredictable. The sort of theory that can account for these facts is very tricky. A shift away from equilibrium theories towards complexity, evolutionary models and agent-based modelling would require massive changes for which students and perhaps academics are ill-prepared.

I'd like to proffer the information equilibrium/statistical equilibrium framework as a theory that can account for these facts without being "tricky".

Information equilibrium is a type of equilibrium, but the underlying information theory (per the abstract of Fielitz and Borchardt's paper) "provides shortcuts which allow one to deal with complex systems" (and has some connections to evolution: here, here). It is a kind of first order analysis with a generalized thermodynamics that lacks a second law which seems to have a connection to recessions. The outputs of agent based models look like information equilibrium relationships.

There are two major regimes in the information transfer framework: information equilibrium and non-ideal information transfer. A lot of standard economics follows from the information equilibrium regime (it leads to straightforward supply and demand as well as a utility-like description). Market failures can appear in the second regime. In this regime, recessions can come from irrational or complex social factors (connected to that lack of a second law) as well as various kinds of shocks. This gives a general view of the business cycle in which recessions are likely unpredictable (like avalanches), but may have probabilistic indicators. However, this is not the only view in the framework (for example, you can understand the economy in terms of just labor and productivity) and the information transfer framework has the benefit of not assuming what a recession is in order to study it (like so many other economic frameworks do: here, here). You can even understand growth in terms of either the Kaldor facts or something that works better.

The "representative firm" is probably an emergent concept in information equilibrium like the representative agent. Additionally, the distributions of firm growth rates discussed in Bloom et al can be understood as the result of looking at ensembles of information equilibrium relationships. Macroeconomic equilibria can be understood as "statistical equilibria" in the economic state space ‒ distributions that are stable over time. The skewed distributions during recessions can be understood in terms of the non-ideal information transfer. The concepts of price stickiness and even stock market prices can also be understood in terms of this economic state space (all at the previous link).

Awhile ago, I put together an outline of an "Economics 101" course that could be taught using the information transfer framework. You might think the math is tricky, but overall it can be understood in terms of the regular supply and demand diagrams with a couple changes: there's another "solution" where supply and demand are tightly linked and move together, non-ideal information transfer turns the supply and demand curves into bounds, and to understand macro you might have to look at ensembles of diagrams (a picture from this link is at the top of this post).

Since this isn't throwing out all of ordinary economics and has a simple diagrammatic representation, it might stand a chance. And it keeps all the hooks for complexity and agent-based modeling. You can even use the framework to understand the classic microeconomic experiments (here, here) and do real forecasting making it more empirical in light of the "credibility revolution".

But one important aspect of the information transfer framework is its plurality. It's a framework, not a specific theory. While I have taken to writing my own models in this framework, there is nothing preventing you from writing down a New Keynesian DSGE model, a stock-flow consistent model, "market monetarism", or even understanding completely different schools of economics.