A rather compelling example (imo) that the Fourth Gospel does play on some "hidden" meaning of egô eimi while using it in the most unremarkable way on the surface is in 18:5ff:
Then Jesus, knowing all that was to happen to him, came forward and asked them, "Whom are you looking for?" They answered, "Jesus of Nazareth." Jesus replied, "I am he." Judas, who betrayed him, was standing with them. When Jesus said to them, "I am he," they stepped back and fell to the ground. Again he asked them, "Whom are you looking for?" And they said, "Jesus of Nazareth." Jesus answered, "I told you that I am he. So if you are looking for me, let these men go."
Another possible echo of this motif is the consistent contrast between Jesus and John the Baptist who constantly defines himself by what he is not (1:20f,27; 3:28).
More generally, as far as the exegesis of the Gospel is concerned, it must be kept in mind that "Trinitarianism" and even the orthodox conception of the exclusive "deity" of Christ are about as much of an anachronism as "Arianism," "Unitarism," or JW theology. The extension of christological expressions to the elect may run against the (4th-century) orthodox view of the Trinity but it reflects a dynamically inclusive understanding of the deity (extending through Jesus to the elect) which doesn't fit the current "heterodoxies" either.