Bednar is not the problem, but the fact you think the losses have everything to do with goaltending, and little to do with all the turnovers, bad starts, bad passes, bad coverage, missed assignments, bad penalties, bad PK, and bad PP, is pretty telling.
In your words, Varlamov holding off LA "isn't saying much" so that means goaltending didn't win them this game.
Somehow, coincidentally they played a near 60 minute game, both special teams were much better, they didn't have a bunch of bad turnovers, they played solid defensively, they stopped leaving their assignments wide open, and they won.
So which one is it? The goaltending that's been all to blame for the losses won them the game? Or the team in front of him played much better than they have been?