And yup, you have again provided no Scriptural support for your personal opinion.
Unfortunately you can't find Scriptural proof texts to define words. To understand things like righteousness and atonement requires careful exegesis of all relevant passages. That's not practical here.
However I can give some references. First, on the righteousness of God in Rom 3:25. Luther's key insight was that the righteousness of God is not "justice by which God is righteous and punishes sinners and the unrighteous", but rather is "righteousness with which the merciful God justifies us by faith."
Martin Luther on the ‘Righteousness of God’ | The Strange Triumph of the Lamb.
The problem is that defending the Protestant concept of God's righteousness really requires a full commentary on Romans, something I'm not in a position to provide. However I'd like you at least to be aware that you're defending the Catholic position, against Luther.
The history of "propitiation" in this passage is more complex. As far as I can tell, Luther's commentary on Romans is not available online. However my understanding is the Tyndale represents Luther's understanding: "Christ Jesus, whom God hath made a seat of mercy through faith in his blood." This goes back to an early Christian understanding of the term "hilasterion" as referring to the mercy seat.
Calvin refuses to decide between this understanding and propitiation. However it's worth looking at his overall explanation:
"it seems indeed to me that he intended, by one single sentence, to declare that God is propitious to us as soon as we have our trust resting on the blood of Christ; for by faith we come to the possession of this benefit. But by mentioning blood only, he did not mean to exclude other things connected with redemption, but, on the contrary, to include the whole under one word: and he mentioned blood, because by it we are cleansed. Thus, by taking a part for the whole, he points out the whole work of expiation. For, as he had said before, that God is reconciled in Christ, so he now adds, that this reconciliation is obtained by faith, mentioning, at the same time, what it is that faith ought mainly to regard in Christ his blood."
That is, he sees the verse as referring to the entire process by which God justifies us by faith, an explanation close to Luther's.
Here's a more technical discussion of the history of interpretation of the key word:
Paul's Letter to the Romans: A Commentary - Arland J. Hultgren - Google Books The author is on the faculty of Luther Seminary, so it's not surprising that he understands it as Luther did.