Could a local app, something like Zimbra Toaster maybe, be used to enable drag & drop of attachments? This is especially needed when multiple attachments are being added. Maybe a "drag & drop" button next to the current "add attachment" button that launches something locally where drags can be dropped, and then relay the pathnames to the web client or something.
Also, maybe that same local app could listen for when a mailto: link is clicked on a web page and trigger the zimbra client to open a new mail window? It's not within the grasp of most users to be able to do this manually.