Hi John Hamman,
I am sorry for the delayed response.
You cannot directly copy the controls from one tab's content panel to another. However, the approach you can use is to associate the whole content panel from one tab to another. The content panel is not copied, but it is rather associated to the different tabs. I am attaching a sample project which demonstrates this approach.
There is also another approach related to moving the controls themselves, but not the whole content panel. I have demonstrated this in a separate project.
If you have additional questions, do not hesitate to contact me.
the Telerik team