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ANSWER: EAD's do not have priority dates. They can only be approved on or after the date you are approved for the status to which you want to change, and which allows for EAD eligibility.
However if your wife is already on J1, you can file for the J2 COS with the EAD concurrently. In Part 2 of the I-539 for COS, you should put the date you want the status to be effective. The USCIS will try to process the application by then, along with the EAD.
Note that it usually takes anywhere from 3 to 5 months for COS, so if you get the application in now, and request that start date, it is more likely than not that it will be processed in time, or shortly thereafter.
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