Grappling with Christ's sacrifice

The ancient sacrificial system makes little sense to me. I cannot relate to the idea of bringing goats or pigeons as an act of atonement. 

But I can relate to the idea of being in deep regret or shame, and wanting to bargain my way out of it, make some kind of substitution, any kind of substitution. What about one of those moments in life that I'd give anything to take it back? I can imagine myself bargaining ... "Anything, I see how wrong it is but there's no way to take it back. Just don't let that ruin everything!" Some people say that bargaining like that is futile, but is it? What if God said "Okay"? What if God took the deal with one condition: He would pay the price instead. 

In some ways, the question of "How could a good God allow evil?" is the question how a good God could allow agency to people who are so flawed. I've heard skeptics and scoffers list their reasons to disbelieve in God, and they are often lists of things that humans do to each other. Even on that level, God bears the shame of any wrong I've done. 

May I consider, in those moments where I feel that urge to bargain away my regrets, that God accepted.