I know there's a scientific explanation for it but the fact that the inductance changes just by shifting the rod baffles me.
This is the kind of stuff that still proves Arthur C Clarke " any sufficiently advanced technology is indistinguishable from magic".
If you place the coil asymmetrically you are getting into the 'end effect' of the ferrite rod, so some of the magnetic field lines will escape and that will marginally reduce your inductance. It's as if you cut off a few windings from your coil. So the coil exactly in the middle has maximum inductance, moving it off to the side will reduce it very slowly until you hit the end, after that it falls off a cliff.
hth.