I appreciate the good sentiment expressed in this, reasonably put. I assure you atonement was provided by Christ alone. The problem I'm expressing is a difficult one, because over centuries of Christianity words have taken on technical meanings, when the biblical language itself was less technical. That's why Luther could not understand James and his sense of Christian works, because Luther read into Paul's use of the word "works" a technical application, meaning self-atonement.
But "works" does not always mean "self-atonement" in its biblical use. Words mean what they mean in context. And so, I'm not trying to stir the pot, but trying to re-focus on John's burden to get us to demonstrate righteousness--not just believe in it.
To say we "participate in our salvation" is loaded with problems, when it is understood, in the usual way, as self-atonement. I was raised a Lutheran--I would normally read it like you do, or as "justbyfaith" does. But in order to clarify, I have to expose the problem. And to do that I have to show how the supposed technical expression distorts an important aspect of our involvement in Christ's salvation. We have to do Christ's righteousness if we truly believe in it! We are not saved if we don't do it!
None of this has a thing to do with self-atonement. It is the necessary response to that atonement, to bring that salvation into our lives. Sorry, it's difficult!
It is certainly by grace--by Christ's free gift of atonement--that we are saved. But it does require that we truly accept it, by putting it into effect in our lives. We need to embrace the new righteous nature he died to give us.
My sense of works is not just a matter of "how we will spend eternity." Rather, it consists of the things we do to serve Christ in our new nature, in terms of being charitable and in terms of fulfilling our ministry. For unbelievers, it may mitigate their sins in eternity and reduce their punishment. Works are the free choices we make to cooperate with God's word, whether many or few. Regardless, it isn't how many good works we do that matters, but only the fact that we receive a new nature from Christ that qualifies for salvation.