So we agree about (1) not working. (2) would violate the requirement for Hermetic targeting without AC, that you need to sense the target, not an Hermetically created image of it. If the magus of (3) uses Eyes of the Eagle only to identify the target of his next spell, and can single it out afterwards by normal sight, that spell would work.
Have a look at TMRE p.94f New Range Line: "The advantage of Line Range is that it extends as far as Sight but does not require that the magus can see the target. However, he must be able to sense it in some other fashion: Hermetic magic cannot in general affect an unsensed target. For instance, the magus may hear someone talking on the other side of the wall." So if the guy seen with Prying Eyes talks and can thus be heard, the Hermetic Geometer can affect him with a R: Line spell, after he made his computations right.