In John 18:6 it seems fairly clear that the implied predicate is "Jesus of Nazareth".
Of course. That's why I classified the usage as ordinary from a purely linguistical viewpoint. The tip to the double entendre (as I perceive it) is narrative.
If Jesus is meant to be claiming divinity rather than identifying himself as Jesus, then the fact is it would have been inaccurate for him to state "I told you that I am he", or, "I told you I am Jesus", in response to the statement they were looking for Jesus. Otherwise he should have said, "I told you that I am divine". The conversation makes much less sense if you think Jesus was claiming to be the I AM and then affirming it. Why did the soldiers not fall down the second time in that case?
This makes much more sense: the soldiers are looking for Jesus. A man asks them who they are looking for. They say Jesus. The inquirer responds boldly that he is Jesus. The soldiers are startled at the self-identification from the famous preacher who is supposed to be on the run. Rousing them from the ground Jesus asks again who they are looking for, and again he confirms that he is Jesus and asks that the others be let go.
Yeah sure.
A debate focusing on isolated texts and starting from a non-contextual problematic (static and exclusive identities, "who is who") and dilemma (either "God" as opposed to "creature" or "creature") is probably one of the worst possible angles to appreciate literature in general and the Fourth Gospel in particular.
An allusive style of writing using ambiguity, double entendre and deliberate misunderstanding is, by definition, not flagrant in any particular context; but becomes evident to the reader/hearer in a more inductive way, by an accumulation of "tips" as he reads and re-reads in a cursory / cyclical way. None is so obvious in itself as to be "undebatable" but once you have started to "see" you see more and more (cf. the blind man!). Which is about the opposite attitude to the use of individual verses as "prooftexts". The Gospel of John (and already, in a different way, that of Mark) is closer to an "initiatic" or "spiritual exercise" than to a theological treatise. It takes either a comprehensive analytical and comparative study of the whole Gospel (where Johannine use of ambiguity in egô eimi can be compared to and illustrated by the use of other ambiguities, e.g. about being born "again/from above," "Son of Man," "resurrection," and so on) -- or simple reading of the Gospel, depending on how your mind works.
But in the end you either "see" or you don't (another Johannine theme). That works in literature as well as in religion I guess.