Total Depravity as a synonym for "total inability" was not a belief of the Early Church until the fifth century when Augustine of Hippo introduced the idea into Western Christianity from Manichaeism, a cult he had belonged to before his conversion. In the three hundred years before him the Early Church fathers never interpreted the teachings of the Bible to mean that man could make no choice. Instead the unanimously and directly affirmed "free will" which did not mean man's will was unrestrained and uninfluenced only that he could make a choice. The Reformer's doctrines came directly from Augustine. The denial of inability is not a denial that man is depraved. It is not an assertion that without the aid of the Spirit men will come to God. It is certainly not the belief that man by his own power can be good enough to be acceptable to God. All of these are straw men.
The Spirit is in the world, working to convince men that they are sinners, to draw men to Christ and to
convince them that Jesus is who He said He was and did what the Bible said He did. Because of this we can listen and yield to the Spirit but we can also resist Him.
But no one in my camp says we do that independently. This is another misconception. In fact, even after we are saved, we cannot behave like Christ or do His will without depending on the Spirit.
The idea is that the price He paid on the cross is sufficient for anyone and everyone but that people must believe before it is efficacious for them. This would have to be the case if one is to keep the universal call of the gospel intact. Otherwise we end up reading all sorts of presuppositions into the text that no one saw for many centuries.
God did not measure out the exact weight of the sins of the "elect" balance that against an exact amount of suffering Christ endured balancing it so parsimoniously that no redemption would be available to anyone else. How could Christ's suffering be so measured and meted out? It is impossible. He paid an infinite price and because of that, anyone who can be brought to believe in Him can avail themselves of the benefits. This makes God both just and merciful. I do not see this as about "everyone in general but no one in particular." Christ's death could save anyone - unless they have already been judged. In that case they have already received either punishment or reward. Your remarks on people in the hereafter thus do not make any sense to me.