I've been looking around some of the Oriental Orthodox-Roman Catholic consultations and dialogues to see what material has been produced. I'll look through some of my books when I get home.
I note that Pope Shenouda III strongly rejects the filioque. And the synods of the churches have adopted the First Joint Statement which says:
"We are agreed also in our understanding of the Person and Work of God the Holy Spirit, Who proceeds from the Father alone, and is always adored with the Father and the Son."
"The meeting began with a paper by Father Brian Daley, SJ, entitled "The Fullness of the Saving God: Cyril of Alexandria on the Holy Spirit," in which he analyzed Cyril's original and complex Trinitarian thought. Alexander Golitizin responded to the paper from an Orthodox perspective. "
Which suggests a couple of papers that might be interesting.
I would have expected that a lot of English language material would actually be more popular and even when dealing with the filioque would not be so detailed as to investigate any statements of St Cyril. Christology has rather tended to be the focus of much English language effort at present.
I guess that a search for specialists in the thought of St Cyril might help.
Just from a few materials around me here at work I note that St Severus says:
"For the Son was begotten by the Father, and the Spirit proceeds from the Father, although eternally and without time, and their ascent is to him, as to a root and source, and from him they are, though they are not after him. And for this reason, while we confess three hypostases, we do not believe in three first causes, but one first cause, and one kingship. After pursuing the matter so far we praise only and do not investigate what the unbegottenness of the Father is, or what the generation of the Son is, or what the procession of the Holy Spirit is; for these things are known only by the Father who begot and the Son who was begotten, and the Holy Spirit who proceeds from the Father: but he requires us to know 'through these things that we are to confess one essence and Godhead, made known in three distinct hypostases. "
"And of the person of the Son who is the wisdom of the Father it is written, -Ãƒâ€šÃ‚Â½I was born before all the mountains-+, and about the Spirit it is said, -Ãƒâ€šÃ‚Â½The Holy Spirit which proceedeth from the Father-+. And the divine Scripture does not use such words at random, saying that the Son is begotten and the Spirit proceeds, but that we may not confuse the hypostases, and that we may know definitely that the Son is one in his hypostasis, and the Holy Spirit another, and that, though they are both from the same essence, and from the same one Father, one is begotten and the other proceeds."
.....and on many more occasions.
I take it that an example of the passages in question from St Cyril is:
"St. Cyril of Alexandria says that "the Holy Spirit flows from the Father into the Son (en to Uiou)," (Thesaurus, XXXIV, PG 75, 577A)."
This seems to me not to deny the one origin of the Holy Spirit in the Son, and as with much modern Roman Catholic thought would support the economic procession of the Spirit through the Son. And this is the teaching of many of our own Fathers.
The very fact that the most devoted followers of St Cyril did not teach a double procession suggests strongly that this was never how St Cyril was understood.
This is probably also why there will be little Oriental Orthodox material on the particular issue of St Cyril's thought. The Fathers never considered that St Cyril taught a double procession, and probably the present bishops would not consider such a thing either.
Perhaps when the OO-RC dialogue comes to consider the filioque it may be raised.
As far as I can see and from my knowledge of the OO communion, all reject the filioque, though I am also sure that theologians in all the OO churches would understand the concept of the economic procession of the Holy Spirit through the Son.
I don't believe any would agree with a view that suggested St Cyril supported the double procession.
But I'll keep looking for something meatier.