Currently, we prevent you from copying a project that is a project. It's a restriction we hope to be able to remove at some point (the underlying reason we currently have the restriction is that our system minimizes the amount of data that gets written when a project copy is made - and we're concerned about possible performance issues if the "levels" of copies gets deep).
What you want to do is totally reasonable and we're sorry it's not as simple as just pressing "Copy Project" at this point. If you come up with a reasonable workaround, please post it! And thank you for highlighting it as an issue - it helps us to prioritize our work when we hear concrete examples of where we're not measuring up to expectations yet.