A Theory of Atonement (Or so it seems to me...)

I've been trying to make sense of the atonement in my own mind for many years, wrestling with two very difficult intellectual hurdles, both of which I believe I am on the way to overcoming. As far as theology is concerned, I am only a moderately educated layman. With that in mind, I submit to you some ideas I've been working on which are now, I believe, developed to the point of peer review. If I have wandered into heterodoxy, please rebuke me kindly.

The problems are these:

1.) How can substitution be truly just? I've heard many times the story of the wise judge whose own son's case is brought before his bench. The judge rules his son guilty and then takes off the robe to pay the penalty on the behalf of the guilty. Fine. But payment with a federal reserve note and payment with blood are hardly comparable. The former can transfer hands easily and the latter can not. It does not appear fair that a guilty life can be replaced with an innocent one. If one's reply is that it's grace, then why require payment at all?

2.) How is one death satisfactory payment for many errors? Even in cases when a serial killer is put to death, justice is not completely served. It's only as close as we can get unless the condemned is a cat who has killed less than ten people.

The responses are these:

1.) My response to the first problem comes from the idea of corporate culpability. Many Old Testament examples come to mind of individual sins meriting corporate condemnation. God seems to view people in perhaps less of an individual sense than the average Westerner does. It seems to me that if one man's sin can be in some ways another man's condemnation, then the reverse must be true. Christ can fairly pay for a man's sin if He, as a member of mankind, is victim to its consequences. Thus, corporate culpability makes subsititutionary atonement logical. Or so it seems to me.

2.) My response to the second problem comes from the idea of infinite personhood. One finite person dies a finite death. But one infinite person would die an infinite death. An infinite death could theoretically be a more than sufficient replacement for any possible number of capital offenses. Thus, infinite personhood makes a single act of atonement satisfactory. Or so it seems to me.

I foresee some objections, but I'll let someone else bring them up instead of battling straw men of my own creation...