(I’m going to change my mind to agree with you on what Paul is talking about here in a minute, Pilgrim. 
But first some other things.)
In regard to salvation depending on some kind of faith living or existing in Jesus’ blood, I’m not sure how to parse that even in Pauline (and general Jewish) terms of the life/soul/nephesh being in the blood. Faith in any case seems rather a categorically different thing.
And while grammatically it might work if this wasn’t supposed to be connected to displaying the faith of Christ, it is supposed to be connected to displaying the faith of Christ. I can’t think of any way that some kind of faith existing in Christ’s blood was displayed by His death on the cross. (Not even with a doctrine of transsubstantiation, friendly to that though I am.) But it’s (relatively?) easy to see how the faithfulness and faith of Christ was manifested and displayed by His voluntary self-sacrifice on the cross even to the fatal shedding of His blood: a faith Paul expects us to share in through sharing the death (by baptism) with Christ.
In regard to going forward a micro-tad in the same sentence to consider the possibility of Paul talking about all humanity not only Jews and Gentiles in the church, by reference to “for all have sinned”: first, I didn’t just randomly fish back several verses, I was trying to integrate Paul’s whole discussion since the beginning of what we call chapter 3 up to this point; and second, I included “for all have sinned” in that understanding, that neither Jew nor Gentile (but especially not the Jew over the Gentile) gets to have a special claim to holiness under God, for Jews and Gentiles both sin and if anything Jewish sin might actually be worse due to having had the Law! – their sin leading to hypocrisy which leads to the nations blaspheming God because of them.
Now, having said that (here comes the place where I changed my mind!): I went back to re-read the whole thing again, and back even into chapter 2 and chapter 1, and having done so I no longer think Paul was primarily talking about Jew and Gentile getting along together within the church (though this may still be a secondary topic). There are several other strong connections to the topic of all humanity which we both agree Paul is talking about later in chapter 5, not least of which is an early statement of Paul about how rebel Jews still have the advantage of being entrusted with the oracles of God, but even more importantly God’s faithfulness toward them does not depend on their faithfulness to Him.
So when he says Jews and Greeks (Gentiles) are all under sin, Paul is in fact talking here like he’s talking later in chapter 5: he’s talking primarily, not secondarily, about the situation of the world before its salvation (whether Jew or Greek) by Christ. Chapter 1 starts off condemning pagans (though with an acknowledgment that Paul owes them a debt in the Spirit which he is glad to repay); chapter 2 transitions from condemning hypocritical and/or unmerciful Christians(!) and talking of the justification as well as condemnation of (evidently non-Christian) Jews and Gentiles both under Christ at the judgment, into talking about Jewish Christians putting themselves back on par with non-Christian Jews by relying on justification through keeping Torah, and thence into a discussion against what non-Christian Jews are doing wrong, even though God remains faithful to them.
Consequentially, that means Paul does mean the same late in chapter 3 as he’ll be talking about (again) in chapter 5: he isn’t primarily talking about the justification of Jewish as well as Gentile Christians by the faith of Christ (as an after-the-fact reality) with secondary comparison to the inability of non-Christian Jews to be justified apart from faith; he is primarily talking about Christ justifying the whole world, all who have fallen.
This runs directly against Calvinistic ideas of election. But an Arminian might be able to reply that so far as this portion of the epistle goes, Paul still isn’t talking about an assurance of salvation.
That depends however on what “justified” means in its grammatic form there. If it’s in the form of an accomplished fact (as Calvs tend to argue, not incidentally), then this could be referring to assurance from the divine perspective: certainly elsewhere Paul treats our justification and sanctification as though these are already accomplished, when clearly as a practical matter they aren’t (since as Paul admits and insists Christians are still sinning, including himself, and including in the Romans epistle). This is exactly why Calvs and Arms have both popularly attempted to appeal to a useful legal fiction of righteousness for Christians, where God just pretends we are righteous by pretending (i.e. by mere legal fiat declaring) Christ’s righteousness counts as our righteousness, and maybe always will do so! An ethically coherent account of this however would be (as Calvs and even some Arms acknowledge) that God is revealing the assured end-result, our being made just and no longer sinners, by treating it as an accomplished fact, since from God’s eternal perspective anything in our temporal future is already accomplished, all times being present for God.
If so, then there is direct (if subtle) testimony to the assurance as well as the scope of salvation here, which would mean this is a specifically universalistic claim, not only a claim shared by both Arms and Kaths (on the scope of salvation).
One more snippet from the best short essay on Romans we’re likely to see:
Even those who know to give the “Lord Lord” and who may be praised by God Himself for caring enough about doctrine to test even apostles, may be thrown into the outer darkness where the wailing is and the gnashing of the teeth; whereas Christ praises those doing good in His name even if they are not following the apostles – while warning the apostles themselves they will by no means be entering the kingdom, but are in danger of being thrown into the unquenchable fire of the tormenters, for thinking too highly of themselves!