That's a good one. As for brakes, there's a few things I can think of that could cause one or the other noise (screeching and grinding), but I can't really think of one commonly associated with both exactly as you describe, especially without pressing on the brakes. First thoughts lead to transmission, drive shaft and rear axle problems, but I don't recall hearing about screeching in that list. In other areas it could be things like belt squeal, water pump squeal or even power steering pump squeal all coupled with worn bearings or pulleys touching something. How those would relate to reverse only I'm not sure. For reverse only problems you have to consider that worn rear suspension is part of the problem, possibly coupled with a worn center support bearing and/or worn motor mounts.

Although I haven't experienced this, I suppose it might be the parking brake shoes binding in the drum area of the rear rotors. That could give the metal-to-metal sound in reverse only, but I'm not so sure about the screeching part. As an experiment you could try to reproduce the screeching in reverse with the park brake partially applied or pulling up on the parking brake while the screeching is happening (maybe keep your foot on the gas a bit to help maintain the screeching). If the noise changes then I would at least focus my attention at the rear wheels.

In any case, your dealer service will hopefully be able to isolate the problem quickly after a road test. There's nothing like an experienced mechanic witnessing the problem first hand.
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Dave -own 940's, prev 740/240/140/120's & quasi-expert only on a good day