Well, it turns out you need a trailing slash at the end of the directory there.
$conf['external_album_folder'] = '/var/www/data/zenphoto';
is invalid (it needs to be $conf['external_album_folder'] = '/var/www/data/zenphoto/'

, well it works but it is not what you would expect. It creates zenphototest zenphototesting zenphotofoo folders. Added on a trailing / and it works now. Without the trailing slash the images never showed up on the web page though, so one part of the code must be assuming that is a directory path, and another part, not checking for trailing slash is using it as a prefix.
You may want to add a check for that, I think the without slash behavior is unexpected.
Thanks,