This is an IP phone, so the signal going into the phone is 0 or 1's.
Interference would result in dropped packets, that gives dead air or chopped audio.
Putting in the 16 feet replacement Cat.5 cord, that's probably going to be coiled up.
If there was any truth to this, it would be even worse!
If you actually want a some serious high tech cord, get a solid core Cat.6e STP cable, fit a single pass split ferrite core about 2 inches from the receiver end, then a double pass ferrite core 3 inches away from the first core (make sure your loop is not exceeding the limitation of the cable spec's). That would be something NSA use on their dearest servers.
This will kill off any RFI/EMI, and reduce the impact of an EMP, though the phone's NIC is built for UTP.
The problem is probably the environment, healthcare appliances can give all sorts of radiation and background noise.
Hum or static would be picked up by the handset cord or the inbound transmission to the system (crap in, crap out).
Have you tried testing the phone outside off premises?
Kind regards
Gunnar
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Mille viae ducunt homines per saecula Romam