I am very adverse to foo, I would not be raising this issue if there was no evidence (though the ASR church only measures the audio band so you won't go far though).
If you use shielded cables you will defeat Ethernet's galvanic isolation (by linking the grounds at both ends), it's the wrong thing to do.
RFI is generated by the equipments (DSP) and their power supplies.
There is some literature available, for example "The Effects and Reduction of Common-Mode Noise and Electromagnetic Interference in High-Resolution Digital Audio Transmission Systems" by
Jon D. Paul:
"Abstract
High-resolution digital audio systems are especially susceptible to sources of electromagnetic noise from the environment, for example, crosstalk from adjacent cables. The noise can induce errors and increase jitter in the recovered clock signal.
We discuss the most important noise sources and their characteristics. Next, we analyze the noise susceptibility of typical transmitter and receiver circuits. Test results are provided for a system with induced common-mode noise. The paper concludes with circuit design, component and application considerations."
Or some Application Notes by Analog Divices engineers, e.g. "Sampled Systems and the Effects of Clock Phase Noise and Jitter" by Brad Brannon or "Analyzing and Managing the Impact of Supply
Noise and Clock Jitter on High Speed DAC Phase Noise" by Jarrah Bergeron.
It's cheap to try too, just buy a new or used small entreprise network switch, mine cost £35 new off eBay.