You only have to download your current ja_zinc_tpl folder, make some changes in the header of the xml file, give your template another name, rename the folder to ja_zinc_2 for example and zip the folder. Upload the new zip via the joomla admin and you have your additonal theme in a new folder with new name and so preserve the original one, while making changes on the new one.
Complete tutorial goes here for basic Joomla template rhuk_milkyway but from as far I have seen in JA Templates, there you will not have to make changes to any php file as it seems, the paths are all set with certain php codes that pull the template name from the xml or so. I haven’t done this yet with a template at all, but it looks quite easy to be done. Worth checking it out.
http://docs.joomla.org/Tutorial:Create_a_copy_of_the_MilkyWay_Template