John,
Storing a ferrous object on a North – South meridian will eventually magnetise it, so an East – West should reverse the process, but not not necessarily quickly. The same applies if hammered on those axes, but not recommended for a measuring instrument!
As you say, the secret is a decaying AC magnetic field. Passing the callipers through a coil carrying AC will provide the decaying flux as the calliper enters and leaves a field the strength of which decreases according to the inverse square law. So as the object recedes from the coil, the field deceases rapidly.
We used to demagnetise crankshafts after crack detection, by pushing them along a roller track, through a coil connected to the AC mains.
Howard