Chrysostom's Remarkable Explanation of Christological Monotheism in John 17:3

For the first day of class in my John course, I will be doing a short devotional on John17:3 where the Johannine Jesus explains “eternal life” as knowledge of “the only true God and Jesus Christ whom you have sent” (NRSV).

I have always wondered how to understand the affirmation of “one true God” and the addition of “Jesus Christ.” Which one is it, John? Make up your mind! One might get the impression that there is some confusion on John’s part here about how to “fit” Jesus into Jewish monotheism.
Today I came across Chrysostom’s intriguing solution (though I get the impression he would not want to die on the hill of this interpretive viewpoint).
Here is the Greek text of John 17:3 (NA27): αὕτη δέ ἐστιν ἡ αἰώνιος ζωὴ ἵνα γινώσκωσιν σὲ τὸν μόνον ἀληθινὸν θεὸν καὶ ὃν ἀπέστειλας Ἰησοῦν Χριστόν.
Chrysostom says, wait a minute, let’s not jump to the conclusion that John is leaving Jesus out of the “μόνον”. What if Jesus is INCLUDED in the μόνον? For support, Chrysostom turns to 1 Corinthians 9:6: “Is it only I and Barnabas who have to work to support ourselves?”: ἢ μόνος ἐγὼ καὶ Βαρναβᾶς οὐκ ἔχομεν ἐξουσίαν μὴ ἐργάζεσθαι;
Here is Chrysostom’s reasoning: in 1 Cor 9:6, the phrase “ἢ μόνος ἐγὼ” does not exclude Barnabas. They are both part of the “only” according to the logic of the verse. So, perhaps John 17:3 intends this as well. Chrysostom does not venture a revised translation, but here is what it might look like if we follow the same idea in 17:3 as Chrysostom associates with 1 Cor 9:6

“Now this is eternal life, that they may know you, only the true God and Jesus Christ whom you sent.”
Is this a good reading? Well, admittedly Chrysostom gives only 2-3 sentences to make his case, so there is much to be considered. Still, it is remarkable, though no one else I know has come to the same reading. I am not convinced, but you have to give Chrysostom credit for being very observant.
For your information, here is the English translation of Chrysostom’s homiletical thoughts on this verse (I put the relevant comments in bold)

 The only true God, He says, by way of distinction from those which are not gods; for He was about to send them to the Gentiles. But if they will not allow this, but on account of this word only reject the Son from being true God, in this way as they proceed they reject Him from being God at all. For He also says, You seek not the glory which is from the only God. John 5:44 Well then; shall not the Son be God? But if the Son be God, and the Son of the Father who is called the Only God, it is clear that He also is true, and the Son of Him who is called the Only true God. Why, when Paul says, Or I only and Barnabas 1 Corinthians 9:6, does he exclude Barnabas? Not at all; for the only is put by way of distinction from others. And, if He be not true God, how is He Truth? Fortruth far surpasses what is true. What shall we call the not being a true man, tell me? Shall we not call it the not being a man at all? So if the Son is not trueGod, how is He God? And how makes He us gods and sons, if He is not true? But on these matters we have spoken more particularly in another place; wherefore let us apply ourselves to what follows.”