Originally Posted by Peter
I see that you've asked the same question over at B-Greek, and I'm sure you'll get some good answers there. In a word, I think you have to take into consideration two things. 1) There's most likely a semitism here. In Hebrew and Aramaic, the introduction of a relative particle ( אֲשֶׁר [Heb] or דִּי [Aram]) basically introduces a subordinate clause that functions in a way that is highly independent (I don't know if you have a working knowledge of Hebrew or not. If you do, please forgive the explanation!). An example:
וּשְׁמַרְתֶּם אֶת־חֻקֹּתַי וְאֶת־מִשְׁפָּטַי אֲשֶׁר יַעֲשֶׂה אֹתָם הָאָדָם וָחַי בָּהֶם
Lit.: "You will keep my statutes and my judgments [that]: the man who does them will live by them". That would have to be reworked into good English by saying something like: "You will keep my statutes and my judgments, by which he who does them will live".
2) As you mentioned, John often uses a neuter, singular to designate what is is fact a masculine plural.
If you take the two things together, you have this in Jn 17.1-2:
δόξασόν σου τὸν υἱόν, ἵνα ὁ υἱὸς δοξάσῃ σέ, καθὼς ἔδωκας αὐτῷ ἐξουσίαν πάσης σαρκός, ἵνα πᾶν ὃ δέδωκας αὐτῷ δώσῃ αὐτοῖς ζωὴν αἰώνιον
"(Glorify your Son, that the Son might glorify you, as you gave him authority over all flesh), in order that all that you gave him (i.e., all those you gave him), he might give them eternal life".
The relative pronoun is the direct object of the verb, and so is in the accusative case (the Father being the implied subject). The referent is the same as αὐτοῖς, which is now a dative (and masc., plur.) because it is that to that referent that the Son gives eternal life.
In a more proper English, this could be translated: "in order that he might give life to all those you gave him".
I don't see how the pronoun could be anything other than an accusative and still give a good meaning. So I think the parsing here is correct.