You are correct that the copy mechanism pulls the details of the document being copied opposed to setting the destined containerID and content ID. Once the user goes to the URL, they will be able to change the document to the desired location.
Unfortunately there is not a tool to pre-set the location of the copied document. However I understand how this would be a beneficial for users and I would recommend you create an Idea for the feature here Ideas for Jive. If you create the idea please let me know, I would like to up-vote it.
Hope this helps.