I understand the Orthodox idea of a temporal as opposed to an eternal procession, and also the logic about how the Son cannot inherit the Spirit's procession from the Father. While those arguments work well dealing with passages where Jesus says he will send the Spirit from the Father, the Father doesn't seem to be mentioned here. So, what is the Orthodox interpretation of these seemingly unequivocal passages?
What's so unequivocal about those passages? The Spirit is spoken of as the Spirit of Christ, and that is what he is. But if your idea is that this phraseology unequivocally indicates "procession" from the Son, I think you are reading that into the text. It's not talking about procession, but "possession" --> the Spirit of Christ
, or "Christ's Spirit" as opposed to some other spirit (e.g., "the spirit of this world"). If I call God "my God" or "the God of me", it doesn't indicate in any way that God proceeds from me, it simply clarifies "whose God" is being spoken of.
When the Scriptures speak of "procession" in relation to the Spirit, it is always a procession "from the Father". The Son says as much.