You conclude your post with “Start with these assumptions and you fix most of the biggest problems with modern economics.”
Yours is the correct way to proceed: to first of all clearly speak out one’s core premises (= hypotheses = postulates = assumptions = principles = axioms). And at this very first step economists fail already. Heterodoxy is a case in point as the title of this thread testifies. At the moment, there is no common core of heterodox economics.
Your approach is in full agreement with the first principle of science: “When the premises are certain, true, and primary, and the conclusion formally follows from them, this is demonstration, and produces scientific knowledge of a thing.” (Aristotle)
However, while your approach is correct in general it is not correct in detail. Roughly speaking, it is not elementary enough. More specifically, your premise #1 is provably false.
This is the correct core of premises
(A0) The objectively given and most elementary configuration of the (world-) economy consists of the household and the business sector which in turn consists initially of one giant fully integrated firm.
(A1) Yw=WL wage income Yw is equal to wage rate W times working hours. L,
(A2) O=RL output O is equal to productivity R times working hours L,
(A3) C=PX consumption expenditure C is equal to price P times quantity bought/sold X.
These premises are certain, true, and primary, and therefore satisfy all methodological requirements. The set of premises is minimal, that is, it cannot be reduced further, only expanded. The set contains no nonentities like maximization or equilibrium and no normative assertions. The graphical representation of the pure production-consumption economy is shown on Wikimedia AXEC31
Under the conditions of market clearing and budget-balancing in each period, the price is given by P=W/R (1), i.e. the market-clearing price is always equal to unit wage costs. This is the most elementary form of the macroeconomic Law of Supply and Demand.
If the wage rate W is lowered, the market-clearing price P falls. If the number of working hours L is increased the price remains constant, provided productivity R does not change. If productivity decreases the price P rises. If productivity increases the price falls. In any case, labor gets the whole product, the real wage W/P is invariably equal to the productivity R according to (1), and profit for the business sector as a whole is zero. All changes in the system are reflected by the market-clearing price.
This has been the first step. With the second step, the conditions of market clearing and budget-balancing have to be lifted. This produces the phenomena of inventory changes (O−X>0 or <0) and of saving/dissaving (Yw−C>0 or <0) and of profit/loss (C−Yw>0 or <0).
To take the economic system as a whole as the analytical starting point is the correct way. To start with assumptions about individual behavior is methodologically incorrect. This blunder is the defining characteristic of microeconomics. It is just the other way round: given the minimalist core propositions (A0) to (A3), one has to proceed top-down by successive differentiation until one arrives at the individual agent.
Conclusions for Heterodoxy: (1) Throw out the neoclassical set of premises [“most of what I and many others do is sorta-kinda neoclassical because it takes the maximization-and-equilibrium world as a starting point” (Krugman)] (2) Take the premises (A0) to (A3) as the common core of the economic analysis. (3) Differentiate the common core, that is, increase complexity successively, and derive all observable economic phenomena and relationships consistently from the common core. (4) Take the first opportunity to test one of the derived complex relationships. (5) If the relationship is corroborated continue with differentiation and solve concrete economic problems, otherwise, look for a new set of foundational premises.
The acceptance of the premises (A0) to (A3) depends alone on the outcome of empirical tests and not at all on whether one likes them or not, and certainly not on any political prejudice. There is no need at all to believe in anything. Constructive Heterodoxy defines itself by superior knowledge and not by belief or political opinion.
Related 'First Lecture in New Economic Thinking'. For details of the big picture see cross-references Paradigm Shift.