I like how this discussion of who one worships has metamorphed into a discussion of differeing concepts of atonement and forgiveness. Yet, I think somehow it still fits, for ultimately better understanding these concepts might help us to better appreciate the similiarities and differences in the original topic.
Anyway, I appreciate the way you talk about good deeds offsetting bad deeds in Islam. From a Christian standpoint that is not what atonement is. We simply don't work with a balance sheet or set of scales. It is more like a test (be it math or spelling) and the standard for passing is 100%. You can say to the teacher that even though you got 1 wrong, that you got many more right. It doesn't change the fact that you fell short of the standard you needed to pass.
Our standard is God's holiness. Surely you don't conceive of God falling short of perfect holiness and then making up for it by doing some holy act. Well, since our standard is God's holiness, we can't make up for a bad deed by simply performing a good deed to balance out our failings.
But what does happen is that, since we understand that on the cross Christ takes on the sins of the world, Christ absolves us of all sin. And, for reasons known only to God himself, Christ's righteousness (which in Christian theology, of course, is God's own righteousness) is credited to us. And in this act of mercy, even though we are in historical fact sinners, we are spiritually justified and in God's eyes no longer viewed as sinners, but rather are seen as sons and daughters of God ourselves --worthy of joining him in paradise on account of our sinlessness.
(BTW -- again for those who seem to keep missing this concept -- this is why those who think that Christians can simply sin without fear because they are "forgiven" misunderstand completely what God is doing in Jesus Christ. We can't do whatever we want, because in being justified in God's eyes, he looks past our sin but into the direction of our heart. That heart is a repentant heart if we have come to faith in Christ and therefore presumes a desire to serve God as Christ did, living in total submission to the Father as Christ did. So, there should not even be a want to sin therein. If there is, then one needs to confess that and continue to seek forgiveness until one has matured enough to where one loves God so much with his heart that it becomes one with the Father's will and one loses even the desire to sin. So, the idea of coming to faith and then turning one's back on God's righteous ways is totally anathema to genuine Christian living.)
Atonement is what you said originally, paying the price. In terms of human justice it is closer to restitution than anything else. A group of kids are playing baseball in the backyard and hit the ball through the neighbor's window. They atone for that act not by doing a good deed and feed a homeless person or even 1000 homeless people. No amount of good deeds can offset the broken window. But the broken window can be replaced, and if the kids do that then and only then they have atoned for their actions.
This gets us to another difference between Christians and Muslims, and that is the twin concepts of original sin and inherited depravity. Christians understand that the sin of Adam and Eve was so egregious that it changed their spiritual DNA at the equivalent of the molecular level spiritually. Since we are all descended from them after that event, we have inherited corrupted spiritual DNA. We all are fallen creatures from the moment of our conception. (Jesus wasn't because he wasn't conceived in the normal way, but supernaturally by God's own action.) Thus, we all stand in need of something that was lost in us even before we were born. Before we had a chance to sin by acts of commission or ommission, we were stained by inheriting this corrupted nature.
As I understand it, Islam teaches think that we are all born as a blank slate, with a zero balance in terms of righteousness (because you do use a ledger sheet to keep track of good vs bad deeds) and born with equal capacity to choose right from wrong just as Adam and Eve had. You think that we are uneffected by their choice. Yet, if that were the case, then I suppose that the best thing to do with a child would be to kill it in the womb, so as to prevent it from ever having the chance to committ a sin, and hopefully no one actually advocates that.
That description of the spiritual blank slate is not where I come down as a Christian. Rather, because I am inheriter of the corrupted DNA from my father Adam and mother Eve, I start out life with a spiritual birthdefect. And the only cure to this birthdefect is not proving how good I can do or be despite it, but to have the whole tenor of my life changed at one's spiritual molecular level. The infusion of Christ's perfect righteousness DNA into my life is what imparts that change. Because of what Christ has done, I am no longer a sinner. I have become sinless, and only now do I reach the same spiritual place in life that Adam and Eve had when they were created. Now, I can follow God like Christ did, or I can sin like Adam did. Now, for the first time, the choice is actually mine and I am accountable for it. Prior to that, the problem wasn't so much that I sinned (though that would be bad enough), but that I simply lived apart from the knowledge and presence of God living within my life.
So forgivenss is something that I seek when I realize I have errored and strayed from my heart's desire to follow Christ in perfect submission to God. But atonement is what restores me to the place in life where I can actually make those choices and follow that desire -- a desire which I understand is also a gift from God, brought to life in me by the presence of the Holy Spirit.