So why not add the proviso that ensures that no one is misled?
If you preach to all and sundry that Christ was presented to be an atonement and that folk should exercise faith in that blood, then you have not made them aware that some men (even some whom you are at that very moment preaching to) have been excluded because no blood was shed for them. Let's not forget that their exclusion (per Calvinism) is unconditional.
How do you think such a message will be received?
The foundation of your rejection of limited atonement (in this thread, anyway) is - I don't believe - a reason to reject limited atonement. In the practical sense, the Calvinist never - that I am aware - says he knows who the elect are (well...there may be some fringe Calvinists who say they do). Likewise, the non-Calvinst will not claim to know intimately the hidden workings of either the heart or of God's plans. Both Calvinist and non-Calvinist will - with sufficient evidence to make them confident (including the witness of the Spirit!) - recognize another believer. Both, in the end, have to simply go by the fruit of a man's life and testimony. So really, the argument is over what happens in the hidden counsels of man's heart and God's mind.
The Calvinist, in avering limited atonement, has taken scripture and determined that to allow for universal atonement means that Christ's sacrifice must be made for everyone - and the determining factor in salvation must be in some beneficial (or meritorious) quality of the individual. Since the Calvinist recognizes that no eternal good can be recognized in anyone except God does the work, they place the determining role in who is saved with God. The non-Calvinist - wanting to protect the free will of man as the determining factor in whether or not man is saved or not, views the atonement as a finished work that can be applied or not - like the blood on the doorposts at Egypt. If a man is saved, it's because he wanted to be saved and he freely chose to be saved. He applied the blood to himself.
The Calvinist waits for God to resurrect the dead, the non-Calvinist waits for the dead to respond. The Calvinist leans on the Word of God to bring about faith and life, the non-Calvinist leans more directly on the individual to get him to see what is available to him and choose life. So at the heart of the Calvinist doctrine is a recognition (if limited atonement is true) that it must be God who determines this - not man. And with the obedience to spread the gospel and preach it to all men, the Calvinist preacher must recognize that he is not doing it - first of all - for men, but for God. Yet neither is it an exercise simply with God in view. Such Calvinist preachers as George Whitfield and Charles Spurgeon did not spare in preaching the whole counsel of God and longing to see sinners converted. But the foundation was not quite the same. Whitefield wept because men were spitting in God's face and did not know or care - not because men were doomed to fire. His love was to warn sinners of their guilt far more than their destination - because that is the root problem. And so if you don't deal with the root problem, what does the sinner care if Christ died for him or not? But find a broken man, a sinner convicted deeply over his sin and hatred of God and you will find a man in whom God works - a man to whom the cross can be preached without reservation or doubt. Such a man will turn to Christ - not because he was told to avoid hell, but because he was quickened by God to his actual condition. The Calvinist says that THAT is who Christ died for.
But go ye and learn what that meaneth, I will have mercy, and not sacrifice: for I am not come to call the righteous, but sinners to repentance.
Matthew 9:13
And what does the non-Calvinist say? That he can't preach the gospel if he thinks that only some are predestined to life. He is more worried about man's free choice than God's holiness.
Preach first the holiness of God and the lostness of man. Preach man's natural hatred of God and his guilt before that holy God. Preach that first and THEN if men are convicted, they are ready to hear about the mercy of God. The love of God for all men. But if the foundation of their hearing Christ is not a total brokenness over their sin - a deep and shaking recognition of how God sees them in themselves - then they will never see the direness of their need and won't properly and actually turn to Christ. They might think it's a good thing to do. They might pray a prayer and assent to what they are told, but are they truly saved? Only in unlimited atonement is someone more or less forced to believe that they are simply because of a few words that were uttered. But because those who believe in limited atonement rest the weight of salvation on a Sovereign God, they spare nothing in requiring obvious fruit (godly sorrow and conviction of sin) and a good understanding of what is happening before even believing the gospel can be applied. There is no basis necessary that all must be equally savable before the preacher can open his mouth. It is, instead, what focus it brings.
I say that all not to absolutely disavow that universal redemption may be true. I don't know the counsels of God, but since I am utterly convinced that unless God build the house (including the foundation) that they labor in vain who build it, I cannot start the doctrine of salvation with conditions (i.e. that it necessarily be universal or that everyone who hears has an equal opportunity to be saved - I don't know their hearts or what God is doing).
Bottom line, knowing whether Christ's blood was shed for a particular person or not only matters when (and if) that person is first of all convinced and convicted of their guilt and natural enmity towards God. If so convicted and presented with the gospel, then the Calvinist would say that their acceptance of the good news is evidence that Christ's blood was shed for them.
So I don't see either the necessity for determining ahead of time whether Christ's blood was shed for the specific hearer since it will be clear when conviction is evident that they are in need of Christ and so will fall upon Him. Those that don't see the need simply won't and in that sense the blood of Christ wasn't shed for them. Were they predestined? That seems to be the secret counsels of God, but then again it is said in several places (Acts and the epistles) that men (some men?) are so predestined.
Sorry if this doesn't seem to conclude well or misses a point. I started at one point and had to step away for a few hours before I could complete it. I will address what is missing if necessary.