It sounds correct: the horizontal perspective induces vertical disparity errors but they are cancelled when viewed from an angle exactly equal to that of the perspective.
That means the pop-right, pop-left phantograms can indeed work, but may be critical in regard to the viewer position. If the viewer looks from a non optimal angle, then vertical disparity would appear.
In contrast I think pop-up, pop-down phantograms should not produce any vertical disparity regardless the angle they are viewed from. By modifying the angle they will show funny perspective effects, but at least no head-aches:-).
All this sounds very interesting. For Stmani3 I have to think if I could set a condition of zero-disparity for a set of points. Perhaps only three points to define a plane.