Hi CX163,
You are correct in saying that a rhumb line makes a constant angle with meridians (true headings).
If you are using only a magnetic compass (to determine the relative position of the Magnetic North Pole), then google is correct.
If you are using True North as your reference, then you either need a sextant and clear nights (to see star Polaris), or an inertial navigation system (IRS etc)
If you have IRS, then you navigate everywhere using Great Circle tracks because that's how it does the maths.
Happy flying