You have a very good system imho

! As you'll see, fine tuning a system is not necessarily an irreversible project. Since your Linn has the Trampolin, it was designed for a more massive shelf as we can't all have light and rigid stands.
All materials have a resonant frequency and will vibrate when that frequency is excited. They also have an absorption/reflection ratio. When they vibrate, they are "ringing". Whether it be a speaker cabinet, a granite slab, a capacitor in the amp or a clock or even a wall, they all vibrate at their resonant frequency.
As you can see, it's quite easy to smear the musical performance even through the finest components available. We all have to deal with the laws of acoustics and much needs to be learned so we can at least choose a viable compromise.
Here's my take on it. A vibrating cabinet or wall acts in the same manner a speaker cone works, it goes back and forth and emits sound. Even a clock or transistor can vibrate and ring.
There's also the part where the signal from vibrating structures will be fed back through the system. Your cartridge is a transducer and will act like a microphone. Since vacuum tubes are known to be microphonic, I think transistor based amps are too but to a lesser degree.
How does it affect the sound? I believe when all these negative effects are added to the signal, they have a tendency to compress the output signal much like FM radio compression. All audio frequencies are affected by resonant vibrations. We get lingering bass notes, buzzing bass... shouty and sibilant mids, harsh highs...It's more difficult to separate instruments, voices...as if they were lumped and averaged out. Just like FM radio, the output signal seems louder. It smears the leading edge of a note and decay is longer too. This masks the finer inner detail of the performance where you can separate instruments or micro dynamics as we might say. When the output signal is lumped, you have no sense of separating two voices and they rarely start at exactly the same time, these few micro/milliseconds are lost. You lose the flow of the performance and its timing...
Using the right materials to evacuate/dissipate the acoustic energy that can paralyze a good system is more a "trial and error" scheme than our ability to set-up gear based on scientific fact. There are too many variables in the equation sadly. I happen to think that metal structures have a detrimental effect on the musical performance but most audio racks offered are metal. We still haven't found directional dissipation acoustic products. If we did, that would be a giant leap in musical enjoyment. How well do we understand coupling/decoupling techniques?
So all you have to do is try it and hear for yourself, you learn more this way. Trust me, I've made more mistakes than most here.
http://www.concertsoundusa.com/hifi_history/documents/rehedeko_recommendations.pdf
This link is one man's opinion on metal stands. He also sells a wood stand so beware

! But the point he makes is still something to consider. In my opinion, metal vibrations are easily fed back into the system through the speakers and electronics. But that's just my opinion.
Hope this helps, you can all bash it, I'm gone for a few days so I don't mind. There is still so much to learn from acoustical behavior of materials/components and I'm no expert. Just my unashamed opinion.