This should be a short list of possible problems. I don't hear well but a rattling noise coming from the front of the car. My guess about any car would be a bad pulley, maybe a tensioner pulley, or one on a pump or compressor. It doesn't rattle all the time, but seems to be associated with the decreasing/slack engine RPMs. Maybe the cooling fans have a bearing that goes out? I thought about a wheel bearing, but it does it when I first start the car, before backing out. I'll go look at it when it quits raining. Can a CV axle make a rattling noise? Can the AC clutch loose its bearing - sound doesn't seem to be associated with the AC being on or off. Does that idler pulley bearing go out a lot? Can't recall but one before, a long time ago.
sounds like it could be something exhaust mount related maybe? that could be related to the change in rpms. It sounds like it only happens while the gas engine is running?