Ek, Dia, En, and Kata

The Reformed Faith maintains that the grace of God is the cause of man’s salvation (WCF 9:4, 10:2), that faith is its alone instrument (WCF 11:2), and that works are the fruit and evidences of a true and lively faith (WCF 16:2).
With this in mind, it is important to note that there is a different meaning applied to the “by” of “salvation by grace” and the “by” of “salvation by faith.” It is somewhat unfortunate that the same preposition is used in both cases when in the former it is in reference to the cause and in the latter it is in reference to the instrument. To more clearly indicate the distinction I often like to say that salvation is “by grace through faith.” These, in fact, are the prepositions used in the English translations of Ephesians 2:8 – “For by grace are ye saved through faith.”
But what of the original Greek prepositions? What can be learned from an analysis of the Greek?
I looked up all of the places in the Pauline Epistles in the King James Version relevant to the topic of salvation that have been translated either “by grace,” “through grace,” “according to grace,” “by faith,” “through faith,” “according to faith,” “by works,” “through works,” or “according to works.” (I intentionally have avoided the Epistle of James as its use of these terms is substantially different from Paul)

All of this can be summarized in the following table:

There are positive statements that salvation is ek/dia/en/kata grace and ek/dia faith. Then there are statements that salvation is not ek/en works.
What then does Paul mean when he says that God will render to each kata works, according to works? With the numerous statements that salvation is not ek/en works, kata works cannot mean that works contribute to salvation.
When preaching on Romans 2:5-11, I was not entirely satisfied with the explanations of “He will render to each according to works” in the commentaries (Calvin, Hendricksen, Lenski, Murray, Bruce) I read. Most commentaries seem to avoid the question entirely and focus on the overall meaning of the passage that God shows no partiality.
Nevertheless, my conclusion was that “rendering according to works” means not that works are the ground of salvation, nor even an instrument, but that as the fruit of our justification the works match up with—or accord with—the salvation we have in Christ. That is, God sees the good works of Christians and God sees the evil works of non-Christians. And that while our works are not the basis of our salvation, those who are saved do good works.
Unless, do some theologians want to say that we are saved by God’s grace, but that we get other rewards in heaven based on our works? This doesn’t seem applicable in the context of Romans 2 since it is about “the day of wrath when God’s righteous judgment is revealed.”
I admit to not knowing the answer. And perhaps some things wrong I’ve said in this post could be pointed out to me by more learned theologians. Maybe here I’m banking on one of the rules of the internet: if you want an answer don’t ask a question, provide a wrong answer and then many answers will be forthcoming.