It looks like you're riding the proper way with the red line. The green line encourages a vehicle to squeeze you in your lane so I wouldn't take that route.
I have this same problem and I'm guessing in most big cities in the world that this is happening. The only thing I can add is to have your hands ready on
the brakes and to practice making really tight turns, since you and the vehicles are both turning right; you might be able to avoid a close call by just
turning at the same time in the same lane. Maybe you're already familiar with the "QUICK TURN", but if you're not this may also help:

http://www.bikexprt.com/streetsmarts/usa/chapter5a.htm