The confusion here is that you weem to think that a double procession means two separate essences. Scriptures tells us that the Father sends the Spirit, and also, that the Son sends the Spirit. But they proceed from the same Divine Essence, the same Divine Principle.
More correctly, I think, we in the West should say "proceeds from the Father THROUGH [rather than "and"] the Son" when discussing the Spirit's procession.
Regards
The Spirit is a Person of the Trinity who shares the same divine essence as the other Two. If the Spirit proceeds form the Divine Essence, then He proceeds form Himself. The trinitarian concept of God involves the Hypostases, not Essence. In the Creed, this is carefully worded that we "believe in One God, the Father..." where the Father and God are made one and the same lest it be confused. Thus when you say that the Spirit proceeds from the Essence (God), He proceeds from the Father. The Creed establishes the proper order of existence of the Trinity, for the Father is the source and cause of all, including the Son and Spirit. Remember that the Greek word used for the procession implies the source or the well, which the Latin procedere lacks.
Kosta's answer basically covers it. An essence is not a source. The source and point of unity in the Trinity is a Person -- the Father, not an impersonal and abstract "essence" or "God in general." The Father, Son, and Spirit are of one essence, and that one essence is uniquely enhypostasized in its entirety in each of the persons -- it is not divided up between the persons.