For the record, I do not believe in "active reprobation". This is the doctrine that God actively prevents people from believing that would otherwise believe. I am not offended by that doctrine, but I do not find it fully supported by scripture.
Unusual as it may seem, but I, as the non-Calvinist, disagree with you on this point. God does in fact blind people from the truth to keep them from believing. Here is the biblical support for this:
Mk 4:10 When he was alone, the Twelve and the others around him asked him about the parables. 11 He told them, "The secret of the kingdom of God has been given to you. But to those on the outside everything is said in parables 12 so that, " 'they may be ever seeing but never perceiving, and ever hearing but never understanding; otherwise they might turn and be forgiven!' "
If Jesus didn't hide the truth in parables they "might turn and be forgiven."
Jn 12:39 For this reason they could not believe, because, as Isaiah says elsewhere: 40 "He has blinded their eyes and deadened their hearts, so they can neither see with their eyes, nor understand with their hearts, nor turn--and I would heal them."
Why couldn't they believe? Because they were being blinded...not because they were born Totally Depraved.
There are many more, but this should suffice for now.
So let's talk about what the Bible actually means when it says that God hardens people's hearts.
Most reformed/calvinistic people such as myself believe that the way the God hardens is by simply allowing sinners to go on in their sinful ways, adding sin to sin in their rebellious hearts. I think even non-calvinistic people can agree to that definition.
I discuss the way in which God blinds people from the truth
HERE. So, I don't only believe God is letting them go on in their sinful ways, as you stated, but more than that, he also is actively blinding them from the truth which might convince them to repent. God might not want them to repent for a time in order to accomplish a greater purpose through their rebellion (i.e. Pharaoh, Israel, Judas etc)
Now, if we can all agree that, in fact, God hardens hearts, then can we all agree that conversly God softens hearts. And if God softens hearts, why does he not soften all hearts?
There are several issues here.
1. Calvinism assumes that men are born in a "hardened" condition...i.e. "unable to see, hear, understand and believe the gospel truth"
But, scripture teaches that men GROW hardened, or BECOME hardened over a period of active rebellion against the clear revelation of God.
2. Because of their view of Totally Depravity (#1); Calvinism assumes that men's heart must be "soften" or "regenerated", in order for man to see, hear, understand and repent when confronted by the Gospel truth.
But, scripture teaches that the gospel IS the power of God unto salvation, it is the message of reconciliation, it is the life giving truth that can set man free. It IS the means of "softening" ones heart, though it is not "irresistible." In that sense, God does "soften" all hearts because he send the message to all peoples. He draws all people to himself.