Right, this gets complicated. On a Mercator map projection, Rhumb Lines are straight, Great Circles are curved towards the Equator. So you would think you would fly RLs. Notso. Think we're going to scrunch up the top of those meridians to a point on the map (North Pole)- what's it going to do to the tracks on it? In real life, because meridians converge to the Poles, RLs are really curved towards the Poles and Great Circles are straight lines. So a plane flying a GC is indeed altering course all the time whilst flying absolutely straight- that's why they are the shortest distance.
So pull yourself together man, this is the nation of Captain Cook, and if he had it sorted 240 years ago, we will get it knocked off now OK? Just be nice to the natives.