The consecrators of Parker, by using the Cranmerian Ordinal, signified outwardly their intention to do something other than what the Church does in consecrating a Bishop. In their case, they were not intending to hand on powers to offer sacrifice and forgive sins and ordain sacrificing priests. Had they wished to do that, they could have used the restored Ordinal that Cardinal Pole had used under Queen Mary.
St. Thomas notes: "Some heretics in conferring sacraments do not observe the form prescribed by the Church: and these confer neither the sacrament nor the reality of the sacrament." (Summa, Pt. III, Q 64, Art. 9, ad. 2)
Your very description of what the heretic Barlow and Company were doing, which is certainly faithful to what they intended, makes clear that they were not ordaining a man to the summum sacerdotium as understood by the Catholic Church spread throughout the world. Give Barlow and Co. credit for what they were doing, which was certinly anything but ordaining a man to the Bishopric in the Catholic sense.
That intention also does not exist in the Russian, Greek and Oriental Churches. If the lack of that intention invalidates the Anglican episcopacy, then should it not also invalidate the Greek episcopacy?
You are very confused. The Orthodox certainly intend to make men Bishops with the power to forgive sins, offer the sacrifice of the Mass, and ordain Priests with the same powers. Not only is this explicitly their faith, but it is very cogently expressed in their rites, the same which are used by the Eastern churches in union with the Pope of Rome. Additionally, the Catholic Church considers the Orthodox Churches as a part of her in rebellion, but not yet completely cut off. The Anglican Church, on the other hand, is a conventicle of heretics, its Anglo-Catholic wing which shares our faith only making this more manifest among the depraved majority.
I had an orthodox priest tell me once that Apostolic Succession isn't just ordination genealogy; it's adherence to the Apostolic Faith.
And to the Apostolic Comunion.
Now we have sliced through the "who ordained whom" discussion and come to the real issues that must be addressed in order for an Anglo-Catholic reunion to work. Those issues tend to evolve mostly around priests. Do priests forgive sins or do they pronounce the Lord's forgiveness of sins? During the Eucharist, does the priest consecrate the elements or does the Holy Spirit consecrate them? During ordination, does the bishop make the postulant a deacon/priest/bishop or does the Holy Spirit do that?