Stacking the odds against a character can also tie into justifying the character and the story to begin with. Jackie Chan always has the odds stacked against him because if he just used his immense skills to beat people up for two hours, he wouldn’t be sympathetic or likeable and the movies wouldn’t be very much fun at all. You have to justify your hero or else your hero is just a bully.

You still have to have 'all is lost' moment to make win much bigger for the audience.

I think you can just escape contrivance if you make the success come at great personal cost. Of course, if the cost is too great it becomes a tragedy.