The more I think about it, your grid is more than one dimension short of reality. If it was light coming from Centauri to Sol, as I make it, that is all the grid itself proves, other than time gaining, light-time history ascending, gaining, between Centauri and the traveler. You have it oncoming to the traveler, time (Centauri's future (+)) oncoming to the traveler at speed, in one, and time oncoming to the observer as usual . . . from Centauri(!), in the other, okay, but it has nothing to do with the possibility of light-time histories shifting into the past (-), ever deeper into past (-), from the traveler to the observer, at Sol, and from the observer, at Sol, to the traveler in the opposite direction.
There are four different dimensions of light-time history involved, not the two only in your grid, Centauri to Sol (which you illustrate), Centauri to the traveler (which you illustrate as a growing, an accelerating, gain into a future (+) . . . okay), the traveler to the observer (which you don't illustrate . . . as a growing, an accelerating, loss into past*-)), and the observer to the traveler (which you don't illustrate . . . as a growing, an accelerating, loss into past (-)). It is in no way a one, or even two, dimensional light-time photo-history picture. It is four-dimensional time, four dimensions of light-time history, four different histories, minimum! Three variations of speed of time, speed of light-time history, passage, not counting the clocks and clock timing, the (two system, locked to the 0-point combine, Centauri and Sol) observers' and the traveler's onboard clock essentially observing gain to future (+) -- to Centauri -- to the fore and loss to past (-) to the rear -- to Sol, in exactly equal parts light-time history gain and light-time history loss., whether traveling at Star Trek-like warp speed or a few thousand years of unpowered speed.
The grid lines between traveler and observer, as time, as light-time history, grid lines, would be continuously widening in distance between grid lines (again grid lines of time / of light-time) as the distance between traveler and observer at Sol continuously widens. For the traveler, Sol, and the observer at Sol, falls into the past (-), eventually four years into the past (-). For the observer at Sol, the traveler falls into the past (-), eventually four years into the past (-) . . . at Centauri. At Centauri, for the observer at Centauri, the traveler comes from the past (-), comes from history (-), light-time history . . . at accelerated speeds. None of it changes the speed of light, or the light-time (the 'photo'-history) distance, between Sol and Centauri, between Centauri and Sol, for any the three participants in the act in the 0-point combine, the quantum entanglement, of the two systems.