It’s usually a good idea to look at what’s normally connected, when breaking a circuit, and replicate that. Which I seem to remember is a 10k resistor with a parallel capacitor (being too lazy to go back and look again). You could try the same combination, in place of the added input cable, on the lines that you plan to use and see if it whines. If not, add the cable(s) and try again. That may stop it happening on all channels.
There are two muting methods - open circuit the input (via a switch or a gate) - in which case there will probably still be some signal transfer through capacitive coupling - especially if the amp side of the open circuit is high gain. Or short the signal path to ground - and that short will have some impedance and thus the signal is only attenuated and not removed all together.
Turning the amp gain to far higher than it ever would be in practice is hardly a fair test. There aren’t many amps that will be noise free under those conditions - and, in this case, there will be a signal to amplify, albeit highly attenuated.
It’s good to be cautious - cascade failure can be waiting to bite. Never direct connect unless unavoidable - add a series capacitor, if you can. Yes, not usually a good idea to provide a dc path unless essential and, even then, current limit it if possible.