I love the subject of shooting on the move and this is an interesting conversation you guys are having. I've been following it, but occasionally get a little lost in all the linguistic descriptions (also pretty tired at the moment so that probably doesn't help.)
I think you both ought to record some video and post it so we can better see what you are talking about.
In any case, when we are talking about whether to stand and shoot, move a little and shoot, or move a lot and shoot, I think it becomes a difficult discussion due to individual shooter strengths and the unknowable element of how well the adversary is going to shoot. That's the part that to me, puts the decisionmaking squarely at the feet of self-perception of our abilities, the degree of alarm we feel in the moment, and the spatial factors involved - available space, available barriers, location of threats, location of bystanders. I personally think those spatial factors should be a primary driver in deciding whether to stand and shoot, move a little and shoot, or move a lot and shoot.
Depending on the circumstances, we might maintain the safest shot angle to bystanders by standing still, moving a little, or moving a lot.
Depending on the circumstances, we might best use a barrier by standing still, moving a little, or moving a lot.
Depending on the circumstances, we might have a temporarily advantageous angle against multiple threats by standing still, moving a little, or moving a lot.
Depending on the circumstances, we might avoid an environmental hazard like a busy street or something we could fall off of, by standing still, moving a little, or moving a lot.
Depending on the circumstances, all factors may not align cleanly, and we may have to decide between a safer shot angle and using better cover, as an example.
It seem self-evident to me that a person with well-rounded skill would shoot the best and the fastest while not moving, somewhat less well moving a little, and less well still if moving a lot. Do we want to get the first round on the adversary sooner, but while presenting an easier target to him, do we want to get the first round on the adversary a bit later, but while presenting a harder target to him, or somewhere in between? Are we shooting them well, in the head? If not, why do we figure the threat is going to be stopped once we start landing rounds?
That estimation also fundamentally involves the capability of the other person, which we might be able to generalize, but I think we'll end up quite incorrect in many specific instances.
But, some people are really good at shooting on the move, and some people are really bad at it, so that might factor into decisionmaking too.
These elements that are unknowable or difficult to figure, where maybe there is or isn't a right answer, are why I like the spatial elements of available space, available barriers, location of threats, and location of bystanders to drive a decision of whether, where, and how much to move, because I think those factors more often yield a 'right answer' than we tend to get from trying to consider our own abilities (which we should know) and the adversary's abilities (which we might generalize but can easily be wrong about.) And letting that 'right answer' about the spatial factors be a primary driver of our specific actions strongly suggests to me that it's a good idea for a person to develop well-rounded abilities in shooting static and in varying degrees of movement, so that we can act in accordance with the requirements of the physical situation at hand, without unnecessary hesitation born of lack of confidence in the skills required at that moment.
So I like all of it! Stand and shoot, move a little and shoot, move a lot and shoot - it's all good. I do like to practice shooting in a fairly high degree of motion and with harder targets. Starting two or three yards away from a bigger target makes the shooting quite a bit easier.