Kinda of cheating since we already talked about this, but here goes anyway...
Scenario 1, 2, 3 -- I fully agree.
Last scenario. Provided the air motor is actually an air motor/pump as stated with the proper mechanics, valving etc. potential transfers unimpeded at its characteristic resonance, cycle time. This scenario is analogous to a capacitor (A), inductor (B) and capacitor (C). The inductor would be the component responsible for managing the magnetic field and thusly would have inertia--once in motion, tends to stay in motion.
Evident from this thought experiment is:
* When energy is transferred, we can use it during the transfer or waste it. Using the energy does not incur any cost to us of the volume of energy transferred.
* When we attach a flywheel to the air motor/pump we don't directly get kinetic (usable) energy. If we tap this energy at all, the flywheel no longer reaches top speed. We ruin the impedance match. The rotating flywheel takes on the form of the pressurized air tank, with the energy now converted, but still potential energy.
Scenario #5 (That you didn't have room on the whiteboard to draw out) -- Multiple air motors inline, in series. If scenario #2 is true, multiple air motors should not change any of the behavior, yet the possibility of performing more work should be considered.
Scenario #6 (Also not drawn) -- A combination of air motor/pumps, some with flywheels and some without.
Scenario # N -- This thought experiment opens the door wide open for all sorts of mutations and modifications along with their electrical equivalent circuits. One of particular interest to me is the parametric oscillation which is by definition over unity.