I think that the advice you've been given is the quickest way to go. You can, however, transfer an existing reservation from WDW to a TA using a transfer form. If the TA is unaware of it, he/she can call WDW and they will explain. This would be the way to go if you are within 45 days of arrival or don't want to pay a second time or wait for a refund. I would also have the TA check for AAA discount availability before you go through all of that.
As far as price differences, it depends on whether you are pricing like for like. If everything is exactly the same reservation-wise but the price is not what you expected, it could possibly be due to the commission paid to the TA. I'm not familiar with the commission structure, but I'm sure a portion of anything you book through a TA (AAA or others) includes some sort of commission amount due to the time, effort and planning assistance provided by the TA. While it may not be the same savings as booking room only yourself at a AAA rate, you need to ask yourself is it worth it to save more than rack rate to have someone else make the reservation for you. Or is it worth sacrificing the savings to book it yourself. The choice is yours and the answer will vary depending on the person.