Whether or not Patriarch Tarasius of Constantinople thought of the procession "per Filium" as eternal or temporal is something that cannot be determined from the acts of II Nicaea.
Again, with due respect, you are contradicting yourself. Does ekporeuomenon refer only to eternal procession, in Scripture and Tradition, or doesn't it? Isn't this the basis on which you say that that word in Greek cannot be used to describe a merely temporal relation? That it therefore cannot be used in the Creed to describe the Spirit's relation to the Son? or do you say there is no difference between ekporeuomenon and processio, both can be used in a temporal sense? Patriarch Tarasius contradicts that because he speaks of the Spirit as "του Πατροσ δια του Υιου εκπορευομενον ("tou Patros dia tou Uiou ekporeuomenon"). Granted that ekporeuomenon always refers to an ontological eternal relation, it follows that Patriarch Tarasius manifestly confesses the doctrine that the Spirit's eternal procession from the Father is mediated through the Word.
Rome defended the formula of Patriarch Tarasius when it was attacked in the West as insufficiently Catholic. Pope St. Leo III who wrote, "The Father, complete God in Himself, the Son, complete God begotten of the Father, the Holy Spirit, complete God proceeding from the Father and the Son" defended the complementarity of the two formulations using from and through to confess the same mystery. So did St. Thomas Aquinas ("because the Son receives from the Father that the Holy Ghost proceeds from Him, it can be said that the Father spirates the Holy Ghost through the Son, or that the Holy Ghost proceeds from the Father through the Son, which has the same meaning") and so does the Council of Florence ("Texts were produced from divine scriptures and many authorities of eastern and western holy doctors, some saying the holy Spirit proceeds from the Father and the Son, others saying the procession is from the Father through the Son. All were aiming at the same meaning in different words.")
The Latin Church has innumerable ancient authorities clearly testifying that the Spirit proceeds from the Father and the Son, Pope St. Hormisdas, "it is characteristic of the Father to generate the Son, characteristic of the Son of God to be born of the Father equal to the Father, characteristic of the Spirit to proceed from Father and Son in one substance of deity", Pope St. Gregory the Great, "The Spirit proceeds essentially from the Son", St. Fulgentius, "Believe most firmly, and never doubt, that the same Holy Spirit, the One Spirit of the Father and the Son, proceeds from the Father and the Son. That He proceeds also from the Son is supported by the teaching both of Prophets and Apostles", St. Isidore, "The Holy Spirit is called God because He proceeds from the Father and the Son and has Their essence ... There is, however, this difference between the generation of the Son and the procession of the Spirit, that the Son is begotten of One, but the Spirit proceeds from Both." ("Spiritus sanctus ideo praedicatur Deus, quia ex Patre Filioque procedit, et substantiam eorum habet ...Hoc autem interest inter nascentem Filium et procedentum Spiritum sanctum, quod Filius ex uno nascitur; Spiritus sanctus ex utroque procedit." etc etc Do you wish to claim the Greek Fathers are in opposition to this Tradition?
While I'm more than willing to let it be a matter of opinion as to whether the Spirit's procession through the Son is either temporal or eternal
But it isn't a matter of opinion, that is the point. It is something we must "believe most firmly and never doubt" in the words of St. Fulgentius. Pope St. Hormisdas' confession of faith describes it as foundational to faith in the mystery of the Holy Trinity.
the Spirit proceeded not from the persons but from the essence
Show me any competent theologian (a king who wrote about in passing doesn't count) in the Latin Church who held that the Spirit proceeds from the Essence, St. Thomas denies it and so does the Fourth Lateran Council, "The substance neither begets nor is begotten nor proceeds; the Father begets, the Son is begotten and the holy Spirit proceeds. Thus there is a distinction of persons but a unity of nature."
It is denial of the Filioque which leads to Sabellianism. Tell me how, in eternity, the Spirit is to be distinguished from the Son? If there is no mutual relationship between the Son and the Spirit, they would collapse into a single Person, since it is the relations between the Persons that distinguish Them. But this is heretical and leads to Sabellianism. Thus there must be an eternal relationship between the Son and the Spirit.
Will answer the point about the fount of Life proceeding from God and the Lamb later. Just one point for consideration now, like St. Ambrose, St. Athanasius also taught that the Spirit is Life and that the Father and the Son are His fount, "David sings in the psalm [35:10], saying: 'For with You is the fount of Life;'because jointly with the Father the Son is indeed the fount of the Holy Spirit"