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Frank asked, "So what real phenomenon are people trying to describe, if any, when they talk about spinning compass needles?"

Here is a hypothesis: While the locally distorted and possibly very strong magnetic fields are static, you (the hiker or surveyor) are on the move. I have an old cheap Boy Scout compass that is undamped, with the low mass jeweled needle in air only. When disturbed, just pulled from your pocket for example, the needle oscillates for an extended duration with an oscillation period of several seconds. If a strong locally distorted field is approached, passed by "tangentially", and departed at a pace that excites to undamped oscillation, perhaps the needle can be made to exceed 180 degrees and impart some rotational inertia. If the strong field is no longer proximate (you have gone by), the needle could make one or several turns.

I just did an experiment with a rare earth magnet on the kitchen table and walked by with the undamped compass. If the speed was just right, I could get a considerable spin going. Too fast or two slow and the needle just deflected transiently. This implies that the disturbance would have to be from an outcropping or some feature that could be reasonably passed in an amount of time consistent with the mode of transportation and the undamped natural frequency of the compass.

See Wikipedia on Circumferentor here: https://en.wikipedia.org/wiki/Circumferentor