I'd bet you can call again and ask to escalate to a manager, and it will work out for you.
But I think for sure you'll need to get a manager: there seems to be much more availability (for most dates, when I was booking my recent trip) for APs than for resort reservation or non-AP ticket holders. I.e., the first line CM probably is told to say no to a request to replace park ressies booked under the AP 'bucket' to non-AP 'bucket,' because it would be an easy way around the sold out ressies for non-AP/resort people. (I also have AP vouchers for everyone in our family, but we used non-AP tix - i.e., I don't think this is uncommon.) The terms/conditions say you have to use the same ticket type(?) to enter the park that you booked the park ressie. So, thus the first line CM saying sorry no. (I'd for sure call and ask to escalate to a manager - just saying a guess as to why the initial attempt went as it did.)