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...as I hinted at before, I think the thing that wins a football game depends very...very heavily on situational coaching and the strengths and weaknesses of your opponent.  You're not going to see that in statistical correlations.  The dichotomy you present between "rush defense doesn't win many regular season games" and "rush defense is PARAMOUNT in the post-season" can be explained by the strengths and weaknesses of football coaches and the tendency for post-season-bound teams to be more well-rounded than the average NFL team.
Against a generic .500 club during the regular season, you're far more likely to be able to find and exploit obvious weaknesses en route to victory (or get exploited en route to defeat).  Example: the Seahawks easily crunched the Cardinals by exploiting the terrified looking rookie QB.  Carroll loaded the secondary with extra help so the rookie had no clear passing lanes and the kid panicked and did horribly.  That's regular season football.  Did the Hawks play much rush defense last week?  No they did not...they didn't need it.
In the post-season, though, you have to be able to stop the run or the other team is going to control the flow of the game and eat time off the clock when it matters.  Playoff games are battles between very-nearly-equal teams with strong rosters and not a lot of gaping holes to attack...at that point it becomes more about who can manage the game better...(head coaches matter here...run defense matters here...effective running game matters here)...who can take away options from the opponent more often, etc.
See...this is what I mean when I say football is a situational game and baseball...really isn't.  This is why there's no signal of clutch in baseball and there's a HUUUUUGE clutch signal in football.  Evenly matched opponents win games by having more options than their opponents...just like in chess (a club level player pursues his plan A and maybe has a plan B...a grand master will CLOBBER this kind of player because he's got 30 ways to kill you in his mind at all times).  Doc...all your stretched chess metaphors make a heck of a lot more sense in football than they do in baseball. :)
My 0.02