As I was able to understand it, the penal substitution view (at least in the Reformed/Calvinist sense) really turned on an understanding of a certain "divine dilemma" for God, in which his infinite mercy and infinite justice had to be reconciled.
Because he his perfectly just, he cannot forgive without punishing sin...or else, so the reasoning goes, he would be unjust. Verses like Exodus 34:6-7, "I am the LORD...a God merciful and gracious, slow to anger, and abounding in steadfast love and faithfulness, keeping steadfast love for thousands, forgiving iniquity and transgression and sin, but who will by no means clear the guilty, visiting the iniquity of the fathers on the children and the childrens children, to the third and the fourth generation" are often cited to support this.
On the other hand, because he is perfectly loving, he cannot completely condemn the entire creation and so therefore must redeem it, and man with it as his own image-bearers.
Therefore, Jesus who is perfectly sinless voluntarily receives the punishment due to the whole human race (which in Calvin's own writings involved rejection from God and actual suffering in Hades, as a condemned person) so that God's justice is satisfied and his anger is taken away from us. They speak of the "double transaction" wherein our total sinfulness is imputed to him and punished on the cross, and his total obedience is imputed to us (well, to the elect, anyway). Jesus of course destroyed death and the power of the devil in his resurrection, and now all who are joined to him by faith are "saved" in the sense that all sins (past, present and future) all already punished...and that Christ's "infinite merit" is now ours, meaning that he's basically earned heaven for us.
I've always thought that penal substitution really only made logically consistent sense in the Calvinist model, where Christ paid the full penalty for those chosen for salvation and no others, lest he shed his blood for anyone who chooses otherwise and therefore "wastes the blood."
Of course this is all caught up in the medeival system of penance, which was bound up with "temporal punishments owed in purgatory," and various sorts of "merit" that could be given to a Christian for good works or acts of contrition, etc. The Reformers were working in basically the same framework but sought to remove the idea that "temporal punishment" always loomed over people...if Christ really took the punishment for us, then he took all of it, meaning there's no purgatory and no temporal debt.
Where that all broke down for me, was that the underlying assumption of what it meant for God to be "just" seemed rather restrictive and human. It treats God's Law as though it looms above him and cannot be transgressed, and therefore forgiveness really is conditional, given only when punishment is served, and therefore isn't actually forgiveness at all. Jesus taught us to pray that God would forgive us as we forgive those who sin against us...meaning freely and totally. We are supposed to forgive without exacting vengeance.
Since all the underlying assumptions are different in Orthodoxy...we aren't born condemned because of the sin of another (whether "real" or "imputed"), God does not have to punish in order to forgive, etc. then the whole model of atonement in the West doesn't even fit.
I'm still learning, and it isnt' nearly as precisely formulated in the East as it is in various Western confessions, which are scholastic and precise and excruciatingly detailed. It seems that Jesus did in fact suffer in our place, accepting the consequences of sin that we'd brought upon ourselves. His sacrifical death did fulfill the entire system of blood sacrifice in the Old Covenant, and what he voluntarily accepted were all the curses of the Law...death, abandonment, being carried outside the camp where the unclean things were (see Hebrews), and so forth. But, just as lepers became clean by touching him (the reverse of the Law, where a clean person became unclean), Christ through his sacrifice made humanity clean again. Death was destroyed in his resurrection. All those who approach God through Christ are clean and holy, forgiven and accepted. His body became the veil that separated the common from the holy, and through him we enter into true communion with God. In the Eucharist we unite ourselves to his sacrifice and through Him offer ourselves to God as living sacrifices. All is fulfilled.
We then struggle against sin, against our own passions, and those things that still try to hold us back (what Paul calls the "old man") in a process of deepening our union with Christ, of becoming what we already are. We are saved, but yet being saved. Holy, yet being sanctified. Justified, yet being made right before God.
"Already, but not yet" and all that.
So far that's the best I can understand of where I am now. The beauty is that all the trappings of merit, punishment, and all the medieval ideas that led to the Reformation and the splintering of Western Christianity, aren't there. I don't need to lay out a billion bullet points of everything Christ fulfilled or did..."he is all, and in all." And I don't need to divide myself from the person next to me because I see the atonement a little more this way, and he sees it a little more that way...we're both sinners, saved by grace, coming to Christ in repentence to receive forgiveness and approach him and truly unite with him, body and spirit, in the Eucharist. It kind of makes your jaw drop and the details kind of fade.
Talk about a "personal relationship" with Christ!