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While your thinking makes sense, you cannot pay anything other than what the court orders you to pay unless the court modifies the order. Failing to pay less than you are court ordered, without requesting a modification, makes you subject to potential contempt charges. The other option would be to work something out with your ex-wife, where she returns a portion the support you paid.
Unfortunately, no, she's not obligated to do this, unless a Judge orders her to do so.