Yep, the 5-pin DIN is also used for MIDI, Tape machines etc. That was (is?) the main audio connector in Europe, where I lived 42 years ago. I built amps using DIN connectors, always 5-pin for 2-channel, did not think much about it, it worked. Typical DIN-5 are not as robust as XLR or Tuchel, but it worked in the consumer sphere. BNC is my least favorite RF connector, but it is OK for audio. There are gobs of RF connectors to choose from depending power level and frequency and passive intermod specs. New types invented continuously.
Right, RFI/EMI is what the shield is for, 60Hz from magnetic fields is very hard to suppress. EMT conduit may work, have not tried.
Ground, or more correctly "bonding" shields to cases can is some instances be part of a ground loop problem. My suggestion would require twisted pairs for signal, and the shield connected to one of the phases at one end. Will not work with coax, where bonding at both ends is the only way for the signal to get thru. The tonearm connector is a bit small, not so robust.
www.calex.com/pdf/4ground_shield.pdf
Above dismissed by
Cable Shield Grounded At One End Only - EMC Standards who did not consider differential signalling, the only subject from the Calex paper. Every Ethernet CAT-5 are differential with transformers at each end, that Ethernet cable could well work with audio signals too. The old RS-485 is differential with terminations, and there are many digital signalling systems using differential with very small signals, to improve noise immunity.
Maybe the cart signal could have a defined potential to shield, like some of the above.
Either way, RCA plugs for phono is not a "good thing".