I found the calculation of the amplitude flows for cases 1 to 4 confusing at first. I think the part I missed is that the reflection of a photon at a half silvered mirror multiplies the configuration (ie the state of both photons) by i. So in case 1 we get each photon multiplied by i twice, so the amplitude at both detectors is 1.
This comment refers to the editor's note in the ebook (footnote 1). That note says that the conventional form of a half silvered mirror multiplies by -1 (not i) when a photon turns at a right angle. The note also states that Eliezer's formulation is physically realizable, but doesn't give further explanation. This seemed confusing to me. If a simple explanation of when Eliezer's version is correct can be provided, then that would be helpful. My guess is that this might be when the mirror is the same from both sides: ex. if the experiment is conducted in a solid transparent medium and the aparatus is constructed by cementing together all the pieces (with the detectors also imbedded in the medium) so that both sides of the mirror have the same interface material.