Toronto tried that with barrie. It was stupid. It's better to go after someone like chychrun and wait until the coach gets fired so that someone can come in and implement a good structure.
Because it didn't work with Barrie in TOR doesn't mean that it can't work, and this is the perfect example of confirmation bias. You make it sound like getting Chychrun would be an easy task. The trade price for Chychrun is going to be VERY high. He's obviously would be a GREAT add, but because of that I'm not sure if the Oilers can (or at least are willing to) pony up the necessary assets to get that deal done.
So the Oilers add more scoring and give up on defense?
In the short term - that would be the direction I would go. I don't think that adding a SAH home guy is going to fundamentally change the Oilers team structure or ability to defend as a team. How do you think that Luke Schenn would look on the Oilers? 15 of the 16 teams which make the play-off's end up disappointed. It would be a "big balls" type move, because it's hard to defend if the Oilers fail and you don't follow the conventional wisdom like "You win with defense". While that is true, I just don't think that the Oilers can change the way they play with 25 games to go, and they're better off trying to outscore their mistakes. YMMV.
EDIT: And for those saying the Oilers should concentrate on defense (which I agree with in principle) - that is pretty damn obvious. I would ask that if it's more likely that the coaching staff hasn't tried that, or if the current roster just hasn't been able to make that work? And if the current roster hasn't been able to make it work, does upgrading Kulak to Schenn (or the equivalent) really move the needle?