"BTW. There will be PLENTY of people all over this world who are alive at the time who will have sin in their hearts not yet forgiven when the King comes back. And also when they die."
You seem to forget that at the moment of the Second Coming, we will be transformed in a twinkling of an eye:
"I declare to you, brothers, that flesh and blood cannot inherit the kingdom of God, nor does the perishable inherit the imperishable. Listen, I tell you a mystery: We will not all sleep, but we will all be changed - in a flash, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, the dead will be raised imperishable, and we will be changed." 1 Corinthians 15:51,52