I always found the best way to explain a critical engine is to explain VMC; the definitions are intertwined, and showing the effects at their most critical time (approaching control loss) emphasises the part each factor plays in making it a critical engine.
I agree too, that in most light twins, the loss of either engine is critical, regardless of the nuances and semantics taught. The loss of the remaining engine isn't nearly as critical as what you do with it while it's still operating. Once it's gone, life gets simple again.
While CG isn't intrinsic to explaining why which engine is the critical engine, explaining Vmc and relating the issue of CG to Vmc will also help illustrate the nature of the critical engine. Torque, "p factor," and other elements are far less important than assymetrical thrust differences...which is the heart of the matter. The bottom line is that in some airplanes, the loss of one engine may be a bigger bother than another.
One way you can also explain it, which works well for a student, is to use a model of a four engine airplane, and explain the differences at each wing station, or for each engine, during a failure. The inboard engines may require half rudder, for example, and less aileron deflection, resulting in higher climb performance, less drag, etc. The loss of the outboard engine may require full rudder, much higher drag, and a complete loss of climb performance...you can establish any performance you want for the model airplane, but it's the illustration that counts in allowing the student to see the difference from one engine to another.
Another handy way to explain it is to put the airplane on a stick, running up through the vertical axis, or the yaw axis of the airplane. Get a model of an A-26 or something with large props to ilustrate the point. Make small arrows and big arrows out of laminated cardboard, with some velcro or sticky tape on the back. With the student looking down on the model, place the biggest arrow pointing back from the descending side of the prop arc, toward the trailing edge, showing where the greatest thrust is...for each propeller. Show which one is farthest from the long axis of the airplane, and which will have the greatest effect or arm. Have the student push the model from each side, and see for himself or herself which has the greatest effect.
It can all be explained verbally, but just like a picture is worth a thousand words, little examples such as that leave an indellible impression in the students mind. If you can explain it to the student, you can explain it to the examiner...and the examiner will be happy. He's not there to hit you with "gotchas," he's there to see it you can teach the basics. Don't attempt to recite what you read in the book; attempt to really teach it, and the examiner/inspector will be happy.
The most effective illustration I've seen in the classroom involved a rotorwing session in which the instructor had me hold a bicycle wheel by the axles, with the axles vertically, as he spun the wheel. He was demonstrating gyroscopic precession, and that simple demo established it in my mind so much better than him telling me. Same for Vmc. Find ways to teach it so the student will remember it...models work really well for that, and you can apply and show all the principles you want on that model. Make it a discussion.
Spiraling slipstream, in my opinion, has little effect on a non-centerline-thrust multi engine airplane. What effect it does have is negligible in comparison to the other elements.
