Well in any case the ships heading did change throughout the trip back.
Of course. Unless you're at the equator it would be impossible to travel a straight line eastward or westward without constantly changing heading. But that doesn't mean you're not traveling along a straight path. On a sphere, in the northern hemisphere, a vessel would have to start by traveling a bit northward, constantly change heading, and end by traveling a bit southward, in order to follow the path of a straight line. The opposite is true in the southern hemisphere. Traveling at a constant heading due east or west, one would have to constantly be turning, and therefore not traveling in a straight line... except at the equator, because the equator is itself a great circle.
Right, that shows why when you take these "straight line" paths from say a flight log, and plot them on a flat map, they appear curved, because the true path IS curved. If the actual path was really straight and flat to begin with, you wouldn't get that effect when plotted on a flat map.
Nobody was ever talking about what the trip would look like on a flat map. Obviously if plotted on a flat map a great circle route would appear curved. That doesn't mean it's following a curved route. It doesn't change that the route itself is a straight line with no turning necessary. Try to keep on topic please.