All tubes are microphonic to some degree. A Herbie's tube damper reduces the vibration of the glass envelope which usually reduces vibration of the critical elements in the tube. It's like putting your hand on a ringing bell. The mass and internal friction of your hand absorbs and converts the vibration motion into heat. Herbies dampers have small amount of internal friction in the soft rubber part of the damper, but mainly the mass does the work by lowering the resonant frequency of the tube envelope to a frequancy that is far below the resonant frequency of the internal parts of the tube where the microphonics happen. Microphonics can cause linear and non linear distortion. Distortion is not always bad, it is just a tool for tuning the system to taste. Few people prefer a very low distortion system for music enjoyment at home, so the sport is all about finding the quality and quantity of distortion that pleases you. Sounds like you have tweaked it to you liking!
The metal tube cover is to protect the tube from EMI, in this case, low frequency magnetic field of the power transformer, and/or high frequency radio signals. The metal cylinder is like a bell, with high Q and low damping so it wants to vibrate at it's specific frequency. The spring also has high Q resonance with low damping. Both are easily excited to vibrate and ring with relatively pure notes for a relatively long time compared to the signal in the tube. The ringing metal causes sympathetic vibrations of the metal parts inside the tube, which affect the sound of the signal. So the metal shield adds vibration to the tube, and the damper removes vibration from the tube, that's why they sound different. On less microphonic tubes, the difference would be less obvious.
You can also damp the metal shield to stop it from vibrating while retaining the EMI protection. Before herbies, people used rubber O Rings for damping tubes. They would sometimes melt onto the tube, but it still worked. The metal shield is much cooler than the tube so a bunch of O rings stretched over top would damp it nicely, or some high temp tape, or use your imagination. Buna-N is common material for o-rings but it has a low melting temp of 250F. That should be enough for a shield or signal tube, but there are others that can take more heat. MSC Direct is a good place to order industrial stuff like that.
Remember that distortion is good, if it is the right flavor, so don't assume that damping all vibration is best. Vibration is a spice, experiment and learn to use it.
In my opinion, if you found a tube that you like, it is worth the effort to give it the extra attention it needs to reach its full potential, rather than choose a lesser tube that needs less fuss. Hifi is an art, and you as the artist, should enjoy the fiddling. The downside of tubes is that they require more attention, but the payoff can be big once you learn their strengths and weaknesses.
