Please answer the question - Is my understanding of W and Gh in your equation correct?
Sorry but no, your repeated insistence in my explicitly reiterating the obvious is vaguely annoying and a waste of time.
What differs, if anything, about my hypothetical "reality" is not the conventional meaning of the standard symbols used in the equation but the assumptions and philosophic underpinnings.
For example, the video posted begins with the assertion:
Now heat naturally flows from a high temperature to a cold temperature and as it flows down some of that energy can be used to perform work.
Your little "black box" drawing is a portrayal of the same old Caloric, flow through assumption.
That is nothing more or less than a reiteration of the old Caloric theory. Carnot's fluid flow from high level "reservoir" of fluid to a low level "reservoir".
We would make more progress if we stop and examine the validity of these assumptions.
Heat is not a fluid flowing "down", through or across, like water flowing "down" a mountainside.. Heat is the transfer of energy (vibration/collision) between unit particles. There is nothing compelling heat to "flow" in any particular direction.
Given two volumes of unequal temperature, there is a statistical tendency for the transfer of energy to progress from the volume of greater energy towards or into the volume with less energy,, but this is not being instigated by any outside force in the same way that water is compelled to flow down due to the force of gravity.
The entire conceptual framework for interpreting and evaluating this circumstance, (volume of energy1 || machine || volume 2) , is a fallacy.
We have simply a thermo-mechanical device situated between two volumes or spacial areas, each brimming over with randomly dispersed molecular kinetic energy, onej ust slightly moreso than the other.
Given this situation, interpreted not from Carnot's old Caloric standpoint, where heat is supposedly compelled to flow "downhill" from hot to cold but instead from the standpoint of the more modern kinetic theory, I don't know of any particular reason why kinetic energy cannot be extracted from two different volumes or sources of energy simultaneously.
If I have two potential sources of energy, why should it not be possible to couple them together in such a way that they amplify each other?
Set up an intermediate space, an "engine" which does nothing but manage energy interactions such that both volumes can be utilized, possibly by setting up an ossillation between the two volumes.
In the world of kinetic energy, something of this sort does not seem entirely outside the realm of possibility, it is only in Carnot's water works, as handed down, that some such scenario has been deemed "impossible".
I think it is about time we clean out the remaining cobwebs of this old Caloric - heat as a fluid flowing down mythos that clouds our thinking in relation to how heat engines may, or may not operate.