There are two judgements, the parcitular judgement that occurs at the time of death of each human being, and then the Judgement Day at the end of times when the world is judged as a whole.
You seem to argue the point that no one is disputing. Christ is the sovereign judge of both judgements; if a non-Christian is ever saved, it is by Christ alone, and yes, it is only possible if the non-believer accepts Christ at the last moment of his life. This is a very intimate moment when a man is judged by Christ, which may justify a life of unbelief. The good works according to natural law do not sway the judgement unless the conversion to the One Holy Catholic and Apostolic Church of Jesus Christ occurs by the movement of the free will. An example of such good works of the natural law and last moment conversion is the Good Thief on the cross.
I am a Christian, non-Catholic so I can’t nor will discuss Cathoic terminology. I would like to let this converation be between those that love Christ, in Kindness and love. You stated “An example of such good works of the natural law and last moment conversion is the Good Thief on the cross”. This was not by human works, but by his FAITH in Christ alone, it was God’s work, not man’s that saved both he and us.
My point in this discussion is that non-Christians (those whom do not recieved Christ’s forgivness becuase they aren’t willing to give up controll of their lives..will not be “saved” by Christ at the judgement of their souls. It may not be PC, but is the truth!