I am using 2 ReadyNAS Duo's and one NV+, I am connecting over AFP, too.
I can delete move or rename images all OK within PM.
Please have a look in FrontView for your share(s).
Go to shares, click on "AFP" for the share in question, go to advanced options and set the share owner (user) again.
Also set in this dialog the "grant delete rights".
What Firmware is your Duo on? I know that the latest release has some issues with AFP.
I am running 4.1.10 T3 (beta version).
Sven