Thank you very much for your hints. This was also the reason for why I could not receive any messages (even with one ZC and one ZED): I just called ZDP_EndDeviceBindReq() once and expected the binding to be successful without sending the message again. Now, repeatedly calling ZDP_EndDeviceBindReq() until binding is successful, I can send messages. And this is also what I will do when a new device joins.
Thank you for your idea concerning a bigger network, too. But first of all I won't have to build such a big network.