OK, let's say that a few find their way though the 'narrow gate'...

OK, let's say that a few find their way though the 'narrow gate' to eternal life in paradise....how does that happen? How is it achieved? Through their own efforts?

It's clearly told in the story.

They pull themselves up by their own bootstraps, became worthy of heaven, no longer being sinners or doing wrong, no longer fallable?

No.
There is a cross involved.