I'm not sure I agree that the amount of string outside of the working length (between nut and tuner and between saddle and end of bridge) doesn't affect tension. The strings are not perfectly fixed nor are they totally immobilized at these points. If they were, you couldn't tune a guitar because the string wouldn't be able to slide in the nut slot.
Maybe it is a tiny amount, but I am sure the strings vibrate outside of their working length, and whether this could translate into a change in our sense of the tension of the string is possible I think. Maybe the contribution of these portions of the string are negligible, but until someone tested it we can't really say.
I wish someone could figure out some other way to construct strings such that there was some way to achieve different pitches besides simply varying the string thickness. Different metal, or some sort of polymer core or something else in materials that changed the stiffness or vibratory properties of the string. It seems we always have to compromise....if we want a smaller scale instrument, for example, we have to settle for more floppiness in strings. Why? With all the technology and space age materials we have, it seems like there should be other ways to make strings besides wraps around a core wire.
Ok it's late and I probably sound like an idiot.