OK, I couldn't find a way around this so I kind of came up with a solution. You can add a new file or directory inside the ZIP file which had the details included.
So, you can use something like:
$zip->addFromString('test.txt', $download_id);
or create a directory named after the download like:
$zip->addEmptyDir($download_id);
Would probably recommend being a bit more obscure with naming though if you get stuck like I did :)
Thanks