How about...
For each owned document, export it to a temp folder
ZIP the contents of that folder to another file
That zip file is a path that is reachable via URL
Open an HTML page, in a new tab, or new window or whatever works.
Use curly braces inside of that to do a replacement as you generate that file to point to the download location of the zip file
Somehow, and I’d have to research it, it would then act like when you go to download a file on the Internet and it brings up a new window, and then after a short delay it brings up a save as dialogbox. Like on sourceforge or github, it says “your download should start in 5 seconds, if not click here”
In summary, you click a button in aware, watch a little spinny thingy, a new browser window will open, and a Save As box will pop up for your download. Depending on your Browser, the download might automatically start and save to your downloads directory.