Okay,
I have now declared my Z-axis sensor dead. Don't know about the compass.
I have contacted the retailer's preferred service partner (in Germany) to ask about the repair/replacement procedure (I would much prefer a replacement unit, if for nothing else then because it'll take shorter, but I expect they have a commitment to try and repair it first). It's going to be a bit awkward since it's across the border and I'm not entirely clear which rules apply. But we shall see.
Next step is very likely to try a factory reset. I shall want to do that anyway prior to sending it to service, but I naturally don't want to do it too soon either -- it's my daily phone/pda.
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Update Saturday morning: Now
all sensors are flatlining
, all three accelerometer axes, and the compass. The "metal detector" app still works somewhat, somehow.