Does the explanation of why slower airfoils are more efficient involve less energy loss from heating or compression of the working fluid?
So you asked a whole bunch of things, and I'm not sure I really understand most of what you are asking, but I can maybe clarify this one part for you


  I have yet to fully understand why "it is better to move a lot of air a little than a little air a lot".


The equation for thrust is just Newton's second law F=$\dot m \Delta$V, where $\dot m$ is mass flow rate (kg/s) and $\Delta$V is the change in velocity of the air (exit velocity minus inlet velocity).  So, if you move 1 kg/s of air at 10 m/s, or you move 10 kg/s of air at 1 m/s, the thrust is the same.  Doesn't matter.

But, the equation of kinetic energy (well power really in this case) is $P=(1/2) \dot m (\Delta V)^2$.  So if you move 1 kg/s of air at 10 m/s, it takes $0.5*1*10^2$ = 50 W of power to do that.  But if you move 10 kg/s of air at 1 m/s it takes $0.5*10*1^2$= 5W of power to do that.  Exact same amount of thrust, but with literally 10X less energy required.  i.e. you need to burn way less fuel if you can move a lot of air at a low velocity than if you move a little bit of air a high velocity.