Huh? I don't even know who Barth is.
That doesn't keep his influential theology from affecting how you read scripture in some manner. In fact, if one doesn't know of him and his doctrines, it's not possible to eliminate them specifically from one's worldview.
But Scriptures say "All died when Christ died". That's Paul, not Barth. Was there a single Corinthian among whom Paul addressed his letter, who already was a believer when Christ died? It was thru Paul that Corinthians became believers. They weren't believers yet, like Paul, when Christ died. Yet Paul said, he was crucified with Christ. So were the Corinthians. They were crucified with Christ, died with Christ. And so with us.
No. One must understand the explicit distinction between articular and anarthrous nouns, especially when they are coupled in sequence as the same word. English doesn't have anarthrous nouns, instead utilizing the vagueries of indefinite article nouns (which Greek does not have). This is the greatest area of misunderstanding and mistranslation by English speakers as comparative grammar.
All as an anarthrous noun is not all as an articular noun. Same "thing", but different reference for content and context. English speakers have to spend time having their mind renewed on this topic if they are to accurately represent scripture. It's an epidemic in modernity.
I felt obliged to read who Barth is. It appears he is a universalist, just like Bociferous in this forum. I think my position is not the same as Barth's.
Barth is not a Universalist, as many misportray; but he takes a position of universal atonement (not universal salvation) that is beyond unlimited atonement in any form.
His position (on which he wrote over 10 million words in 14 volumes) is that all died with Christ and are alive in Christ to be able to repent. He was attempting to resolve the same seeming paradox you refer to for Arminians and Calvinists, etc.
His problem was that he wasn't a Greek scholar, much like St. Augustine wasn't a Greek scholar (along with many others). None of these understood the difference between articular and anarthrous Greek nouns. And this is also your source of confusion in coming to some gradient of the same conclusions as they did.
Barth believes all will finally make it to eternal life, no matter what. I don't.
That's a misrepresentation. Barth is not easily understood, as he intermixes many views he opposes to illustrate his own; and the distinctions aren't clear. Further, he has been mischaracterized by those who have not copiously read his work, and many have erroneously presumed him to be a full-on Universalist (Universal Reconciliation). He is not.
I believe that because of what God through Christ has done for humanity in his life, death and resurrection, all had been saved, are being saved, BUT only overcomers will finally make it to heaven and eternity. All others will suffer the wrath of God and finally thrown into the lake of fire.
This is basically aligned with Barth, and it's fallacious. And predominantly because the English heart and mind has been patterned to replace Greek anarthrous nouns with either English definite article nouns or English indefinite article nouns.
This point of grammar is huge, and one who does not understand this cannot validly dismiss it OR readily comprehend it. It's an epistemological foundation of basic lingistic function, and it has been the pattern of thought since the womb and all stages of development into adulthood.
It's not a small issue, and it's the main reason for the proliferation of beliefs within Christendom for the last half millennia or longer.