I defer to your musical expertise, and everything you said makes a lot of sense. One idea that came to me while listening to the video was wondering if pressure on the key controls how much pressure is applied by the string against the bow as a way to let the performer vary the sound. That might be a partial solution to what you're describing.
As a mechanical engineer, I have to respond to your terminology. The tension in a bow is the same all along the length of the bow. It has to be; it's the force the bow hair applies to the connection points at both ends, and if it wasn't the same along the whole length parts of the hair would be pulling harder than other parts which isn't physically possible.
I think the effect you're describing has to do with pressure perpendicular to the bow: how hard the performer is pressing the bow against the string. That deflects the bow hair, and for a given pressure there's greater deflection in the middle of the bow than at the ends. Also, the deflection changes the tension all along the bow, which changes the sound.
I can definitely see how you'd think the tension is different at the ends of the bow, because your feedback is the sound that is made and you can only measure the tension at one point of the bow at a time. Assuming you're applying equal pressure, when you measure the tension at the ends you're getting a different result than when you measure in the middle, because the deflection is different. If instead you reduce the pressure to near zero you should hear the same sound all along the length of the bow, because you have constant (zero) deflection and constant tension.
As a mechanical engineer, I have to respond to your terminology. The tension in a bow is the same all along the length of the bow. It has to be; it's the force the bow hair applies to the connection points at both ends, and if it wasn't the same along the whole length parts of the hair would be pulling harder than other parts which isn't physically possible.
I think the effect you're describing has to do with pressure perpendicular to the bow: how hard the performer is pressing the bow against the string. That deflects the bow hair, and for a given pressure there's greater deflection in the middle of the bow than at the ends. Also, the deflection changes the tension all along the bow, which changes the sound.
I can definitely see how you'd think the tension is different at the ends of the bow, because your feedback is the sound that is made and you can only measure the tension at one point of the bow at a time. Assuming you're applying equal pressure, when you measure the tension at the ends you're getting a different result than when you measure in the middle, because the deflection is different. If instead you reduce the pressure to near zero you should hear the same sound all along the length of the bow, because you have constant (zero) deflection and constant tension.