Electrical – Averaging electret microphones’ inputs

I expect you are right about what the wires are. You should check with a voltmeter though to make sure. Ground should have the lowest voltage, power the highest, and the return audio somewhere in between although it may be almost the same voltage as the power but at a higher impedance. If you load the audio line with 10 kΩ or so, it should drop a bit whereas the power line should not.

By the way, unless you have specific documentation that says these are condenser microphones, I think they are more likely electret. However, that doeesn't matter for the purpose of extending the cables.

I would use stereo shielded cable to extend each microphone. Obviously the shield should be tied to ground. Since you're only going 8 inches, I don't expect any significant problems with that. Try to leave as little length as possible for the audio wire outside the shield.

Here's the circuit you linked to with a couple of red circles on it: -

Check that capacitor C1 isn't somehow leaking some DC current through to the -Vin pin.

Also check that R4 is fitted correctly and you can measure the same voltages on each of it's pins as you do on the op-amp pins. R4 could be broken - can you measure it with a meter?

Measure that copper tracks are fine between R4 and the op-amp.

If necessary lift C1 from the circuit to check that -Vin and +Vin become the same level.

The OPA345 is unquestionable a good device for this application if you don't care too much about noise. The AD8606 does the same but will produce less noise.