That would for sure be a neat addition to their existing functionality. Actually it's quite surprising they don't have something like that in place already. I think the quickest, easiest, and least client-side annoying way to add 'zipping' ability would be from their backend by installing PHP's ZipArchive extension. Possibly prompt the user on download if the file should be compressed, create an instance of a ZipArchive, and then step through your directory structure adding files using their built in ZipArchive::addFile ( string $filename [, string $localname ] ) function.
You mentioned using something with Jinzora? I've never heard of that, so I googled it. Since you mentioned PHP, I assume they're using PHP too to run their media server stuff. This being the case it seems logical that they would require PHP's ZipArchive extension to be 'installed' on the server running an instance of their media server.
PHP's reference page for the ZipArchive class:
http://us2.php.net/manual/en/class.ziparchive.php
I'm not brushing off the idea, I'd love to help you implement that if you're into it. I just thought I'd outline what I think would be the easiest way to accomplish your goal.
Let me know what you think.