I apologize for being so stubborn about this, but I think it ultimately is important given my (current) belief that everyone might be, in some sense, “elect.” Of course, that’s a whole ‘nother discussion…

Throughout the Gospel of John, the group of people that the Father has “given” to the Son is a broader category than just the disciples who are actually following Jesus during his lifetime. Yet, on your reading, “those the Father has given to the Son” would have to be limited to the 12 disciples (or at least only those who believed during Jesus’ ministry). I don’t think that does justice to this theme in John’s Gospel overall, nor to the theme of the prayer in John 17 (which picks back up after v. 20 with referring to even this latter group as those the Father has “given” to the Son in v. 24). Here are some examples:

“All that the Father GIVES me will come to me, and whoever comes to me I will never cast out. 38 For I have come down from heaven, not to do my own will but the will of him who sent me. 39 And this is the will of him who sent me, that I should lose nothing of all that he has GIVEN me, but raise it up on the last day. 40 For this is the will of my Father, that everyone who looks on the Son and believes in him should have eternal life, and I will raise him up on the last day.” (John 6:37-40)

“My sheep hear my voice, and I know them, and they follow me. 28 I give them eternal life, and they will never perish, and no one will snatch them out of my hand. 29 My Father, who has GIVEN them to me, is greater than all, and no one is able to snatch them out of the Father’s hand. 30 I and the Father are one.” (John 10:27-30)

And again, even in John 17, Jesus begins by noting that “you have given him authority over all flesh, to give eternal life to all whom you have GIVEN him”, which de facto includes anyone who comes to believe and who enjoys salvation (just as in 17:24).

So I’m still persuaded that the not-yet-existing believers in 17:20ff are a subset of this larger Johannine category of the elect, of those the Father has given to the Son.

As for #1, I would actually argue that the (future) group of people Jesus moves on to pray for in the final part of his high priestly prayer are a subset of “those the Father has given to the Son”, not of the world. In praying for them (in the future), Jesus IS praying for “those the Father has given to me.” They just don’t exist yet. I don’t, then, think he is going back on not praying for the world; that always remains true in the sense of this prayer’s ultimate purpose. He prays for his own, that they might go into the world and bless it. And within that world are sheep of Jesus’ fold who have not yet come home…but who will (John 10:16ff).

Just a couple comments and questions:

1. In John 17, Jesus first prays not for the world, but for those whom God has given him (v. 9). Then, in vv. 20-26, he prays for another group of people, “those who will believe in [him] through [the original disciples'] word” (v. 20). This leads me to believe that you cannot identify the people for whom Jesus prayed in v. 9 as the elect, because those mentioned in v. 9 are only a subset of believers.

2. I understand that you are trying to steer clear (temporarily) of questions about election’s meaning to focus on its function, but I have to think that our answers to questions about the former will inform our understanding of the latter. (4), for example, brought all sorts of questions about perseverance of the saints to my mind.