Have you compared this Variax to any others? What you describe is what some people have heard in the older version of the Variax guitars. This is the sound of the piezo pickups picking up the sound of all the noise around the bridge and your picking resulting in the sound you hear. It can be more noticeable when palm muting, like you said. It is the nature of the Variax guitars.
This has been greatly improved in the James Tyler Variax guitars.
i agree with hugo. most likely a result of the metal case of the lr baggs pickups. one piece of metal against the saddle and also against the bridge plate . metal transfers sound best.
graphtech pickups are enclosed within a composite saddle. a switch to those may cure this.