That which Christ breathed into the Apostles is Pneuma Agion, the Holy Ghost (or Spirit), the third person of the Trinity.
We do not dispute that the Holy Ghost proceeds from the Father. We noticed that we had received it not directly, like Moses received the Ten Commandments, but rather from Christ the Son. It is not incorrect to omit the Filioque, but if said, it refers to John 20:22.
All the difference between the two Greek verbs that you point out does is to suggest that the relevant passage of the Creed should read, "We believe in the Holy Spirit [...] that proceeds from the Father and is given us by the Son". This would be quite verbose but would accord with "ekporevetai" in Jn 15:26 and "lavete" in Jn 20:22. I do not see any substantive objection to this formula.
The giving of the Holy Ghost by Jesus to the Apostles is a temporal event which is altogether different from the eternal (unchanging) relationship of the Triune God -- the Son is eternally begotten (the Word is eternally generated by the Wisdom) and the Spirit of God eternally proceeds from the Father.
You are using a temporal event in the created world as the eternal manifestation of God. It's apples and oranges.
Your attempt to find a better wording is a violation of the Ecumenical Councils. It would be equivalent to taking a dogma proclaimed by the Pope ex-cathedra and adding one word to it because it 'sound better" or something to this effect. Can a Roman Catholic, frewillingly alter Propes dogma to suit someone's taste? Of course not! The pronouncements of the first seven Ecumenical Councils, the basis for the undivided Church, which are recognized by the Latin Church without exception, are binding even to the Pope because they are pronouncements of the Church (at the time when the Pope was not the king -- and I realize this is difficult for the Romans to accept the fact that the Pope did not always rule the Church). So, nothing can be changed, added or subtracted to any of the infallible pronouncements of the Ecumenical Councils.
This is not a matter of taste or discussion. Addition of filioque was a violation of the EC pronoucnements and as such are heresy.
Let me try again and then its off to bed. First, a quick observation. Your comment that we do not receive the Holy Spirit directly from God like Moses for example isn't borne out by the Eastern Fathers at all, for example St. Basil the Great, St Symeon the New Theolgian, St. Gregory of Nyssa, etc., but I think I know what you mean.
I think we can agree that God is essentially unknowable, ineffable and completely transcendant. The Trinity is of one ousia which is shared in by three hypostasia. God for the Eastern Fathers was always thought of as "Trinity" and that Trinity sent the Son, Who was "begotten of the Father before all Ages" for the salvation of the world. The Latin Fathers tended to look at God (as opposed to the ousia of the Father being shared with the Word and the Spirit) as a unique essence first and only thereafter of God as Trinity. In Latin theology, the divine hypostasia become really nothing more than expressions of the inner relations of the ousia of the Godhead. Now, if this were so, then the very existence of the Holy Spirit can only be defined and determined by its relations to both the Father and the Son. Logically then, filoque must be true and absolutley necessary because there could be no distinction between the Spirit and the Son unless the Spirit proceeded from the Son, and vice versa I suppose. The Greek Fathers viewed this doctrine as a form of Sabellianism wherein the hypostasia are merely "modes" of a unique "God". The Greek Fathers taught that the Father is the only source of the Deity, the Son having been begotten by Him and the Spirit "proceeding" from Him. Because the Son and the Spirit are "omoosios" with the Father, each has His own existence and function both in the inner reality of God and in the economy of theosis. Filioque, in this theology, which was the theology of the One Church for 800 odd years, reduces at least the Spirit (and perhaps even the Father and the Son too) to a mode of some different God than we worship .
I have given some thought about your posts and perhaps Kosta has gleaned where the problem is. The relevant section of the Creed dealt with refutation of Christologic and Trinitarian heresy. It speaks to the "inner and outer nature" of the Trinity. It doesn't deal with what goes on in the here and now. Thus, the difference between "ekporevetai" in Jn 15:26 and "lavete" in Jn 20:22 is very important since these words efer to different things. Ekporvetai is dealing with the the Spirit in the same manner that the English words "begotten not made" deals with the Logos, though of course these are not at all the same concept. "Lavete", liturgically translated as "take" as opposed to "receive" is a temporal imperative form. In other words, it has to do with us in the here and now. Procession has nothing to do with us nor with time. One might be able to say "through the Son" in a non exclusive sense regarding the "lavete" matter, but of course that doesn't talk about the nature of the Trinity and in any event, none of us, from the Pope on down, can sua sponte change what the Church decided in the Council and which was received and accepted by the people. Does this help?