You ask: Does the evangelical tradition objectively say what Jesus considers to be the greatest source of His glory? Not that I am aware of, although Protestant evangelicals believe in the triune nature of God. While on earth, Jesus purpose was to glorify his Father in heaven and this he did by being obedient unto death. In so doing, Jesus was glorified by God the Father. The glory of one is the glory of the other:
”The Son is the radiance of God’s glory and the exact representation of his being, sustaining all things by his powerful word. After he had provided purification for sins, he sat down at the right hand of the Majesty in heaven” (Hebrews 13).
The Protestant evangelical view of the meaning of John 13:31 is that the glorification of the Son of Man (Jesus) and the glorification of God (the Father) are inextricably intertwined by virtue of the fact that Jesus (Son of Man and Son of God) is part of the One Being of God.
Jesus gave up the glory he already had in heaven, alongside the Father, in order to be born of a woman (John 1:14.) As you point out (in John 17:5), before his death Jesus prayed to his Father to be glorified in God’s presence with the glory he had before the world began. This glorification occurred at Christ’s resurrection and exaltation to God’s right hand (Hebrews 2:9). The Bible also speaks about future glory, when Christ returns “in the glory of his Father” (Matthew 16:27).
As to what Jesus may have considered to be “the greatest source of his glory”, John chapter 12 gives us a few clues. This event happened after Jesus’ triumphal entry into Jerusalem before the Passover. Jesus tells his disciples:
”The hour has come for the Son of Man to be glorified” (John 12:23).
This does not mean a literal hour, or at that specific moment in time. Jesus’ words refer to what is about to happen – his betrayal, his death, his resurrection. Jesus speaks of “the hour” to which everything else has lead, the culmination of his ministry on earth. The glorification comes as a result of his death, resurrection and exaltation. This is borne out in Jesus’ next words when he acknowledges the reason he has come to this moment in time:
”Father, glorify your name!” Then a voice came from heaven, “I have glorified it, and will glorify it again” (John 12:28).
Moving forward to John 13:31, after Judas goes out to betray Jesus, there is no turning back. Jesus knows that events have been set in motion that will lead to his death, and through his death and resurrection, God’s plan of salvation will be accomplished. That is why he could say:
”Now is the Son of Man glorified and God is glorified in him. If God is glorified in him, God will glorify the Son in himself, and will glorify him at once” (John 13:31-32). NOTE: Some manuscripts do not have verse 32
The glory is all about the vindication of God’s sovereignty, God’s holiness, righteousness and justice. Jesus’ sacrificial death on the cross and his resurrection will result in salvation for all who come to saving faith in what God, in Jesus, has done to defeat sin and death. The glory of the Father and the glory of the Son are bound together because they, along with the Holy Spirit, are one in unity and one in purpose. God is the King of Glory (Psalm 24:7-10) and Jesus is called “the Lord of glory” (1 Corinthians 2:8): “None of the rulers of this age understood this, for if they had, they would not have crucified the Lord of glory.”