Funny how this mysterious culture always appears in hindsight. Every team that is ever successful apparently has it, but it doesn't exist anywhere until the moment a winning record does, when suddenly it's been there ever since the signing of <guy you like>. Management and media have talked about everyone the Oilers have brought in as these good character/culture guys, hell, the big knock on Chiarelli was that he overvalued/overpaid his "culture" guys relative to how much he liked his "talent" guys. Steady stream of culture brought in, but it all magically becomes bad culture when it turns out that a guy sitting in his office saying nice things doesn't cause Milan Lucic to suddenly skate faster or be able to handle a pass.
The history of the NHL is full of dirty players, guys with drinking problems, guys with drug problems, guys who were unpleasant to deal with, guys who beat their wives, guys who slacked off half the season, guys who straight up didn't care to try to play defense, and what they all have in common is that the ones who won stuff get called great character guys. Guys like Guy Lafleur, Paul Coffey, Mario Lemieux and Wayne Gretzky largely didn't care much when the opponents had the puck, which sounds like the exact kind of culture you *don't* want to perpetuate...but they all won so it must be a great idea to approach the game that way. Think about that next time someone accuses McDavid or Draisaitl of cheating for offense, they're just trying to emulate the 80s Oilers culture! Encourage them to never play defense, it builds character!
Or maybe culture is just a label people apply after the fact to try to convince themselves that winning and losing is defined solely by how good of a person you are because it sounds nicer than acknowledging that some guys just flat out don't have the talent to be good at the NHL level.
I mean, we could always trade McDavid. Team's been bad with him, and since good culture can never exist on a bad team, he's obviously a bad character guy. Ditch him and get Hendricks back, that ought to help.