Jesse: Thanks for the hint!
For reference, /path/to/dir/**/*zip*/foo.zip downloads a file named foo.zip with the contents of /path/to/dir (i.e. no top-level directory named dir in the zip file). /path/to/dir/*/*zip*/foo.zip downloads all the files in the directory dir, without sub-directories.
To conveniently download these, enter the pattern ** or * into the box in the path bar, see a preview of what you're going to get, and only then click the download link.