If His death and resurrection is not the determining factor in my justification then what is?
It is, but justification/reconciliation goes far beyond my individual salvation. The Western Church has individualized salvation to the point the atonement has become all about me and me alone (or the elect and the elect alone). But that is another discussion for another day.
Do you think we should not try?
As long as the "effort" is not elevated to the status of absolute, comprehensive, propositional truth (which often happens in systems like Calvinism). We must always remember the effort is a human effort to explain a divine mystery that cannot be fully grasped by the human mind.
The "L" I embrace is "Limited Understanding" which reminds me that no human system has it all figured out. There are aspects of the atonement and its final implications that we will never grasp.
It really doesn't say that much.
Yet it says enough to say that what Jesus did was more than enough to cover the sins of the "world" as described in certain passages and yet effective enough to cover the sins of those who embrace Him through faith.
did God intend to save those whom He knew would never believe?
I believe it is unfair to prescribe to God human categories of "knowing" and "intention". God's purpose will be fulfilled. The means by which they will be fulfilled cannot be thwarted. Yet the means by which God fulfills his salvific purposes cannot be restrained to a human explanation either.
The atonement obviously goes far beyond our individualized understanding of it because as I pointed out before, God is reconciling the world to himself. Our human qualifiers cause us to fit such statements in the context of our theological systems, but I am not sure any of us truly grasp what verses like 2 Cor 5.19 mean.
If we cannot wrap our minds around what happend in the incarnation, death, and resurrection of the Son of God, I am not sure we should be so dogmatic on the "limits" or "definiteness" of the atonement. Again it fits well within a nice, cut-and-dry, 5-point system. But does it capture the whole image of reconciliation/atonement/salvation described throughout Scripture? No.
Remember God did not leave us a systematic theology textbook. He did not leave us a question-answer workbook. He left us a story -- His story, a story of God's interaction with human beings. That story invokes human language, illustrations, life situations, poems, songs, etc. to try and help us capture the relationship between God and humans. It is a divine story inspired by God, but its format leaves us with a mystery element with which we must wrestle and struggle. Simply put, it reminds us God is God and we are not.