As an avid Doctor Who fan of 30+ years standing, I am well aware that there is a fundamental difference between time and space. We all get to travel in both of-course, although time generally in one direction.
The tide issue adds in time, which does not apply to the frontal system which is assumed fixed in space.
So, following the magenta line, time does not affect the wind (apparently nor does height, which is clearly unrealistic), only distance.
However, at sea, time affects the tide. So, you know that the tide will change in a particular way at a particular time. So, you can allow yourself to be swept downstream, knowing that you'll come back this way when the tide changes.
Coming back to the magenta line through a front - constant heading is clearly not the best route and unless you are really clever with your maths, will not get you where you want to be. So, time to destination is infinite. However, constant TRACK, requiring heading changes whenever the wind changes, should still in my opinion be the fastest route from A to B.
G