I believe that to correctly align the overlays, the compass needs to be a rate compass rather than a basic fluxgate type.
this from Wikipedia:
The basic fluxgate compass is a simple electromagnetic device that employs two or more small coils of wire around a core of highly permeable magnetic material, to directly sense the direction of the horizontal component of the earth's magnetic field. The advantages of this mechanism over a magnetic compass are that the reading is in electronic form and can be digitised and transmitted easily, displayed remotely, and used by an electronic autopilot for course correction.
To avoid inaccuracies created by the vertical component of the field, the fluxgate array must be kept as flat as possible by mounting it on gimbals or using a fluid suspension system. All the same, inertial errors are inevitable when the vessel is turning sharply or being tossed about by rough seas. To ensure directional readings that are adequately stable, marine fluxgate compasses always incorporate either fluid or electronic damping. An alternative is to use a 3-axis fluxgate magnetometer to provide a 3D flux vector, and the magnetic heading is derived from the flux on a plane perpendicular to gravity, thus providing immunity from pitching, and rolling.
Fluxgate compasses and gyros complement one another nicely. The fluxgate provides a directional reference that's stable over the long term, apart from changing magnetic disturbances, and the gyro is accurate over the short-term, even against acceleration and heeling effects. At high latitudes, where the Earth's magnetic field dips downward toward the magnetic poles, the gyro data can be used to correct for roll-induced heading errors in the fluxgate output.
The latter is a rate compass, I believe, a combination of solid state gyro (piezo) with a compensated 3-axis fluxgate magnetometer, an example being the Simrad RC42
