You are wrong on the Orthodox.
They do not ALL use the term “purgatory” but they do believe in the possibility of purification after death, and they have no problem with, and encourage, prayer for the dead.
http://www.davidmacd.com/catholic/orthodox/pugatory_orthodox_church_catholic_church.htm
I take the Orthodox at their word. They do not believe in purgatory.
As Kolokotronis said in his post 81...
"The Church of Constantinople rejects completely the notion of purgatory. It is a matter of faith that no soul can, by any action after death including suffering, affect its eternal destiny. We spend eternity with God after the Last Judgment not because we in any way are worthy of that but rather because of God's mercy.
"The Orthodox Church does not believe in purgatory (a place of purging), that is, the inter-mediate state after death in which the souls of the saved (those who have not received temporal punishment for their sins) are purified of all taint preparatory to entering into Heaven, where every soul is perfect and fit to see God. Also, the Orthodox Church does not believe in indulgences as remissions from purgatoral punishment. Both purgatory and indulgences are inter-corrolated theories, unwitnessed in the Bible or in the Ancient Church, and when they were enforced and applied they brought about evil practices at the expense of the prevailing Truths of the Church. If Almighty God in His merciful loving-kindness changes the dreadful situation of the sinner, it is unknown to the Church of Christ. The Church lived for fifteen hundred years without such a theory."
No Orthodox uses the word “purgatory” to describe anything we believe in, K58. We do indeed pray for the souls of the dead in that we ask God to show mercy on them, to forgive their every sin because there is no man who lives and does not sin and to establish them where the Righteous repose, but there is absolutely nothing that the souls themselves can do or go through to alter their eternal situation.