I’m not sure I’m understanding your setup (I only skimmed the post). Are you using takeoff to mean something like “takeoff from now” or (“takeoff from [some specific event that is now in the past]”)? If I look at your graph at the end, it looks to me like “Paul Slow” is a faster timeline but a longer takeoff (Paul Slow’s takeoff beginning near the beginning of the graph, and Fast takeoff beginning around the intersection of the two blue lines).
I’m not sure I’m understanding your setup (I only skimmed the post). Are you using takeoff to mean something like “takeoff from now” or (“takeoff from [some specific event that is now in the past]”)? If I look at your graph at the end, it looks to me like “Paul Slow” is a faster timeline but a longer takeoff (Paul Slow’s takeoff beginning near the beginning of the graph, and Fast takeoff beginning around the intersection of the two blue lines).