Your recognition that the moment of entanglement is the same moment as the moment of detection is brilliant! I have been puzzling for years about the fact that from a photon's frame of reference, emission and absorption are simultanious and the universe is two dimensional. Entanglement adds a new dimension, literally, to this fact. There is a lot more to learn about all of this.

Also, I believe that the world line picture that Tim talks about is equivalent to the one you point out , but I like your description better. Tim is publishing this new realization, and I think that is wonderful.

One more thing. Things are not quite so simply put for massive particles.