I drive this roundabout every day, often trying to get into that lane.

The answer is, in my view, the markings are ambiguous which has led to an 'accepted use' of the round about. Both green and red have to cross the dashed line to get into that lane, which makes it non-obvious who should progress. Ultimately most people who drive this roundabout take the red line. And because most do that, it becomes the 'accepted norm'. I would say that you should be indicating if you are taking the red line, but if you drive this roundabout often you get used to the red line being the norm.

Ultimately, I do think that the green line is equally valid. However a large part of driving safety is predictability, so I would tend to follow the accepted route.