Calibration [with 8-shaped motion] works pretty much ok without TOHKBD (although it seems not be spot on) but immediately goes south (pun intended) with it attached. Also, after deattaching TOHKBD the 8-shaped motion does return the north bearing to approximately where it should be.

[...]

So, it would seem that SFOS compass is not as crazy as I've thought it to be, I just need to "pack lighter" when I need it. What I don't really understand is that how the static magnetic field can have this kind of an effect? Does it e.g. scale the sensor readings so much up that rounding errors start interfering with the calibration, or what? I also noticed that the kind of "corrective motion" that is seen after turning the phone around quickly without TOHKBD is missing when it is attached (to find an analogue from mechnanical compass, it is like the needle is not floating freely).