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Is it meaningful that Jesus called him "Simon, son of John" the last recorded time He spoke to him (Simon)?

Not really, if you're arguing that Simon is not really Peter the rock because Jesus here does not include that name. He's already referred to as Simon Peter in the same text, Simon "the Rock". When Jesus gave Simon the additional name "Peter", He wasn't saying Peter was a physical rock, a mineral substance, and that Simon had ceased to be. He was using a metaphor to express a profound truth about Peter's new calling, to be the Rock (or foundation) on which the Church was built. He was still Simon, but now with the additional name of Peter. Throughout the New Testament he is called Simon, Simon Peter, or just Peter.

If you're proposing here that Jesus forgot that he had earlier called Simon by the name "Peter", well then you've got a whole other problem. That's the only argument that I could think of to assert that this verse has any bearing on the question of Peter's primacy. Another argument, I suppose, would be to say that Christ is somehow "taking back" the name Peter and the keys and the power of binding and loosing. Is that what you're trying to say, because there's no Scripture anywhere to suggest that. The fact that Jesus calls him Simon here and not Peter proves nothing.