In fact, it is probably the greatest source of vibration. However, this twisting vibrational mode appears to be excited when the scope is moved. One way to resist vibration is to increase stiffness. However, another possibility is to use rectangular tubes. Rectangular tubes provide the greatest stiffness of any geometry given the same mass and diameter.
Cylinders are almost as good.
Overall, it adds about 10 lbs, but it is a lot stiffer. To be most effective the second constraining member should be approximately the same stiffness as the first member and cover at least half its length. The completed scope is shown. The difference is remarkable. Once I made the modifications, they damp out within a second.