Goood afternoon, this is Ed.
I must say that although I'm not sure where it'll end, I'm intrigued by your problem. If you don't mind, let me gather a little more info from you to be used by Brain or me and we'll see what happens.
My take on the moan sound is that it really is being made by a pressure differential of some sort, most likely vacuum decaying. Since idle control has much to do with air control, you might have some sort of air leak that is variable, confusing the everlovin crap out of the idle control system. I'm wondering if it might be a PCV valve that sticks in the high-flow position, creating at first an elevated idle from increased airflow, then causing a low pressure area to be built in the crankcase. The theory falls apart if your makeup air tube that leads from the front valve cover to the air cleaner is open and free, but it's a thought. You might want to check the air tube for being free-flowing all the way from the air cleaner into the crankcase by physically blowing through the air cleaner end of the tube. It should offer little resistance.
Likewise, you should feel a small amount of vacuum on this tube with the engine running as the PCV valve purges crankcase vapors. If it feels more like a WOOSH than a sip, the PCV valve may be sticking open at times. As a vacuum reservoir, the crankcase would be the very largest one on the vehicle.
I had a V10 truck once upon a time that had sucked out its lower intake gaskets and was cavitating the crankcase without symptom, except for this noise much like what you've described. The 8-liter's noise was coming from the rear main seal, which was being made to vibrate like a musical instrument from the air being sucked past it.
If the noise is being caused by a vacuum leak from the intake manifold, a quick opening of the throttle blade once the engine is shut down will stop that in a heartbeat. Give that a try -- kill the engine and if it's wailing away, give it wide-open throttle to see if it changes anything.
Another vacuum reservoir is the brake booster. Pumping the brakes a few times will dump the vacuum and stop the noise quicker than if left to its own devices otherwise.
If the noise is electronic (and I keep going back to the coil failures), be sure that the key is all the way off first. If it is still making the sound, turn the key back on, just to see if it changes anything.
Like I said... interesting.