Random hiss that comes and goes with mic/cable position.

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As others have said, it sounds like spurious RF is being demodulated, especially since 500 megohm impedances and high Gm transistors in sensitive circuits of course don't play well with RF. The fact that it's much worse at night sounds like it could even be a distant RF source being bounced right to your location by nighttime ionospheric RF propagation. I used to have a guitar amp that very clearly demodulated the signal from a 100,000 watt AM station a thousand miles away in Mexico, but only did it at night.

Don't forget the possibility of noise being picked up from switchmode power supplies, as well as commutation noise from the small electric motors in things like refrigerators. I know it's highly unlikely, and they probably wouldn't sound like pure white noise anyway, but stranger things have happened. If you have a portable AM radio with an internal rod antenna, it's easy to pinpoint such sources with it as the antennas are highly directional.
 
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Interesting that you say to put the shunt caps as close to the semis as possible - I usually see them mounted right on the XLR pins. I always thought that was to short the RF to gnd as soon as possible.
RF becomes an audio problem only if it's demodulated somehow, which requires a non-linear process (a fancy way to describe any semiconductor junction such as diode, transistor, or vacuum-tube). Since we don't know whether the RF "antenna" is the wiring of the electronics or the cable, this approach stops the RF at the semiconductor, where it would otherwise be demodulated. Since the most common "demodulator" is the base-emitter junction of a transistor, it's a good idea to put a small-value ceramic capacitor between those two terminals of a transistor. Also remember that, at GHz frequencies, smaller values (generally between 20 pF and 100 pF) have lower impedance than larger values like 1,000 pF because of lead wire resonances.
 
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