Well, I've now filmed the experiment and the result is here
(Sorry, I don't know how to get the video to embed in this software …)
The hypothesis I'm attempting to support is that the line's constant velocity (and thereby, its momentum) at the time the rod stops and tension in the rod leg are the main factors that initiate and propagate a loop and hence complete the cast.
The method I've used is to create a situation where the fly leg has a measurably constant state of motion and tension in the rod leg is easily demonstrated.
What you're seeing initially looks like a "normal cast". In fact, it's simply the line laid straight on the road from the end of the rod tip and the rod tip then pulled back along the axis of the fly leg. When the camera is moved with the rod tip so that all movement is seen relative to the tip, the experiment demonstrates that tension in the rod leg is all that is required to initiate and propagate a loop, and that the loop is maintained until the fly leg disappears.
Just before Stage A, the line is in tension.
(In the experiment, the tension is opposed by drag on the road.)
When the tip stops, the line maintains its state of motion.
(In the experiment, it lays "motionless" on the road, but that is a constant state of motion. All line outside the tip has the same velocity as the rod tip at this point.)
When the tip is held stationary, the line continues with its constant state of motion and a loop initiates.
(In the experiment, the tip begins moving back long the road, which means the line is now moving forward relative to the tip
As the line continues to move forward relative to the tip, tension in the rod leg causes the fly leg to cease the forward motion of the fly leg and a loop is formed.
(In the experiment, the line is being dragged back along the road by the tension in the rod leg.)
The fly leg continues moving forward at a steady velocity until the fly leg disappears and the cast is complete.
(In the experiment, the line is dragged into the rod leg as I walk backwards along the road. The fly leg remains stationary on the road, however, relative to the rod tip,
it continues to move forward at walking pace.)
With the experiment complete at this point, the "cast" appears to be a normal cast when shown at speeds approaching those we are used to. When it's "slowed down" to actual speed, it's easier to see what happens in reality. This is one instance where using a moving frame of reference helps to clear up some of the questions. (At least, it does for me. I'm sure others will not agree. That's fine - I'm not going to argue the point.)
This is an easy experiment to replicate by anyone with a fly line, a rod and a carpet or nearby road. Concentrate on the rod tip, watching the line with peripheral vision to focus in that frame of reference. You'll see the line unroll just as it does in a normal cast. Then flick the line along the road too and notice the similarity between the two "casts".
If I had fed line off my reel at the same speed as I walked (as if I were shooting line in a cast), the loop would not have continued to propagate. Without tension in the rod leg, the rod leg has the same velocity as the fly leg and the loop stops. (In this example, I'm ignoring rotational momentum within the loop. I believe it is inconsequential compared with the other forces in play.)
If I had fed line out at a speed less than my walking speed, the loop would still propagate. While there is a difference between the velocities of the rod and fly legs, the loop will move along the line.
If we were to cut the line after the loop had been initiated and while the line was shooting, both the fly leg and the rod leg would have velocities. Newton told us that those velocities will be maintained because there are no (substantial) external forces acting on either leg. (If the fly leg were moving forward at 3m/s and the rod leg at 1m/s, both would continue at that rate, and the loop would move forward at 1m/s relative to the rod leg.) This is clearly shown in earlier videos.
Sorry for the long post. It takes more than 2 sentences to explain some things though.