First, thanks for the sample project, it really helps to get to the problem quickly. Also, you can always open a support ticket if you want to attach something.
I did not know that you are using Silverlight 3.
There you need to add not the popups but their children in the participating visual roots collection.
Also the drop query is a two-way handshake, i.e. the source can decide to that it does not want to be dropped somewhere. Therefore you need to handle the DragQuery event with status "DropSourceQuery". If you do not want to manage this case, you can add a handler to the root visual in your application that will always return true in this case, then you only need to manage the "DropDestinationQuery".
I modified the project you sent me and I am attaching it here.
I was debugging the application though a remote desktop connection and the drag/drop was lagging a bit. I could not figure out whether this is due to the remote connection or something else. Do you see any noticeable lag?
Please get back to us if you see unexpected issues with Silverlight 3 version of the controls.
the Telerik team