the door is closed permanently when we face G-d in judgement after death...
We are certianly in agreement on that point... My only disagreement is that our Lord will never display the human emotion of exasperation the rich man showed with those who cannot follow a simple plan (until, as you point out, it's too late)...
I will not argue with that part. But remember, it is only a story. I won't even call it a parable.
Shalom.