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The first thing you did was to replicate the existing research (yes...existing research) on payroll inequities.  We have indeed run those numbers.  If you take the Yankees and Red Sox out of the per-team payroll calculation, the AL and NL are nearly equal.  The problem is...the Yankees and Red Sox concentrate so many top talents that they force the rest of the AL to up their games and acquire less expensive free agents who can provide nearly the same level of production if they want to compete in the post-season.  The AL teams have to work harder because they are fighting the two juggernauts in baseball.
The interleague imbalances began with the rise of the Red Sox as a second payroll monster and as a world series winner.  I don't think that's a mistake or a coincidence.