I'm not sure what you're not seeing a choice between doing what is right in our eyes or trusting in God with all of our heart by doing what is right in His eyes. Refraining from having homosexual sex is an example of how someone can choose to trust God with all of their heart instead of doing what is right in their own eyes.
Our salvation is from sin (Matthew 1:21) and sin is the transgression of God's law (1 John 3:4), so living in obedience to it through faith in Jesus is the content of His gift of saving us from living in transgression of it. For example, honoring our parents through faith in Jesus is the way that he saves us from not honoring our parents, and refraining from having through faith in Jesus is the way that he saves us from having homosexual sex, which has nothing to do with saying that Jesus died in vain. In Titus 2:14, Jesus gave himself to redeem us from all lawlessness and to purify for himself a people of his own possession who are zealous for doing good works, so becoming zealous for doing good works in obedience to God's law is the way to believe in what he accomplished through the cross (Acts 21:20), while returning to the lawlessness that he gave himself to redeem us from is what mean that he died in vain.
James references both Genesis 15:6 and Genesis 22. The Bible clearly speaks about multiple justification events, which is only problematic to someone if they refuse to accept the truth that we can have multiple justification events. Like justification, our salvation and sanctification also have past, present, and future aspects. Abraham believed the promise starting in Genesis 12.
