Thanks. The long run was installed ... well, when Cat 6 and 6a were the latest thing and I've learned a helluva lot about shielding and grounding since then.But that shield provides a connection between two ground points with different potentials, and will certainly result in current flowing from one to the other, something I have been advised to avoid. I believe you will hear an improvement if you add a LAN Isolator between the router and switch, to interrupt the continuity. A good one will also clean the signal from the router.
For what it's worth though, the network cable connects 2 DC devices. I'll still have a poke around LAN isolators though; I never entirely trust either theory or practice so enjoy the interplay of the two.
The 2 DC powered devices are network switches. One is in what I usually call the Servant position, just after the router and this separates the audio playback chain from any potentially noisy (and non-audio-related) devices attached to the router. The other switch is at the business end of things: a Master switch which connects into my Innuos streamer.