How do I clone a subtheme?

I have a zen subtheme built in the normal way from STARTERKIT. Let's call it mytheme. It works well.

I want to clone it so I can play with some changes without disturbing my current theme.

Here's what I've done.
Copy the mytheme directory to mytheme2.
Rename mytheme.info to mytheme2.info.
Change the name in mytheme2.info
Edit template.php and theme-settings.php to change mytheme to mytheme2 in all the places which were originally STARTERKIT.

Cleared cache. Rebuilt theme registry.
Went to admin/build/themes and selected my new theme.

I can tell by the CSS paths etc in the output that it's still running the old theme.

What else do I need to do?

Thanks