silver, check out rule #3 for calculating probability amplitudes:
It basically states that in order to calculate the amplitude of a photon going to 1 is a product of the amplitude of it going to A and then from A to 1. So we do need to remember what the amplitude was for a photon going toward A.
Great post, Eliezer! I have one question, though, and maybe some of the folks here can answer it as well: why do we multiply amplitude in Figure 2 by i if it either turns "left" or "right" at 90 degrees? In the complex plane, we multiply a vector by i if we want to rotate it 90 degrees clockwise, and by -i if we want to rotate it 90 degrees counterclockwise...