A few comments stand out to me Richard:
... difficult to express, measure and depend on in a given situation.
... to get things started in a properly performing hitch.
... to get the friction process going.
... just the right amount of leverage must be specified when acceleration changes. I don't know how to do that or specify that in a device.
The fundamental element is friction, regardless of what self belaying device is in use. Technically, friction is entirely dependent on the normal (perpendicular component) force applied between two surfaces. For friction hitches we think about this as in how tightly wound the hitch is around the climbing line. With mechanical devices, most of them simply pinch or bend the rope. I would think that the "spring" in consideration is better thought of as a trigger.
With mechanical devices I bet a quantitative analysis would be easier than we might think. Of course the wear on the device will eventually change it's behavior requiring a fresh clutch or links, but over the course of testing I'm sure any one of the regularly used devices would provide enough consistent behavior for meaningful results. Since the geometry for each mechanical device is more or less fixed, it probably reduces the number of variables. However, for friction hitches, the analysis may not be as bad we think since each properly dressed hitch also has a consistent geometry.
The first consideration for a friction hitch test is the coefficient of friction. This is largely an empirical quantity that depends on the materials (types of rope) as well as the interface (roughness). Even though this coefficient has a dependence on temperature, for the purposes of engaging the hitch, we can initially ignore that as a variable. Several other factors such as moisture, dirt, melt, will change this value. For the purposes of testing though, I bet that value would be consistent for a given setup during testing. I think the second quantity to consider would be the stiffness (resistance to bending) of the hitch cordage. We all know that as a rope is used, this factor changes. This last summer I bought some 9mm Technora to try as a hitch. For the first few uses it was horrible. The stiffness of that stuff when it's fresh is impressive. It did eventually "break-in", but I went back to the RIT simply because I like it better in every way. As you have mentioned several times, simply twisting the hitch cord can affect friction. It also has an effect on the stiffness. Lastly, the tightness of the hitch comes into play. As a big climber I cannot climb on a 3-1 distel. It simply tightens up too much after I've loaded it a few times and I end up needing to redress it for it to flow properly. However, with an extra wrap up top (4-1), I hardly ever have to redress the hitch. You know what the difference in the 3-1 and 4-1 is? How
tight those wraps are on the climbing line. My weight doesn't change, the cordage doesn't change, the interface doesn't change (much). The amount of friction the hitch provides is the same regardless of how many wraps are in the system. With 4 wraps up top the amount of normal force for each wrap is reduced and the hitch doesn't become too tight. Of course if a hitch cord is worn adding a wrap will often help with creep, but I believe that has more to do with the freshness of the cord in that extra wrap (restoration of the initial coefficient of friction) than with "adding" force.
All of this is to say that the proper amount of friction will keep free fall from happening. All of the reputable posts and references I've learned from stress how important it is to
have a properly dressed hitch. To me that translates to there being enough initial friction in the system so as to trigger the hitch into tightening up on the rope so you don't fall.
(an attempt at humor, not a wize crack) 
