Thanks for your kind words and I'm really glad to hear that you are finding our WordPress appliance useful, albeit with a little bit of pain for your desired setup...!

TBH, I'm unfamiliar with WordPress multi-site hosting, but I see no reason why it shouldn't work.

My guess is that it's the default Apache config. As you can see the default config explicitly points all incoming traffic to /var/www/wordpress.

If you want to use Apache to direct incoming traffic to different places, then I suggest that you remove the 'ServerName' directive from the top of that file (/etc/apache2/sites-available/wordpress.conf), then within the 'VirtualHost' section add a new 'ServerName' entry there, with the domain you want to server the existing WordPress from. You'll want to do that for both port 80 and 443 (http & https). So assuming a domain of "www.example.com", your resulting wordpress.conf would look like this:

<VirtualHost *:80>
    UseCanonicalName Off
    ServerAdmin  webmaster@localhost
    ServerName www.example.com
    DocumentRoot /var/www/wordpress
</VirtualHost>

<VirtualHost *:443>
    SSLEngine on
    ServerAdmin  webmaster@localhost
    ServerName www.example.com
    DocumentRoot /var/www/wordpress
</VirtualHost>

<Directory /var/www/wordpress>
    Options +FollowSymLinks
    Options -Indexes
    AllowOverride All
    order allow,deny
    allow from all
</Directory>

To add an additional site (let's say www.example.net) which points to a doc root of /var/www/new-site, I'd just copy the existing virtualhost and edit it accordingly. I.e.:

cp /etc/apache2/sites-available/wordpress.conf /etc/apache2/sites-available/new-site.conf

Then edit that and swap all instances of '/var/www/wordpress' to '/var/www/new-site' and instances of 'www.example.com' to 'www.example.net'. Here's how I'd do it (manually doing it is fine, I'm just showing off my ninja commandline skills! :)

sed -i "s|/var/www/wordpress|/var/www/ne-site|" /etc/apache2/sites-available/new-site.conf
sed -i "s|www.example.com|www.example.net|" /etc/apache2/sites-available/new-site.conf

Obviously in your context, you'd want to adjust the things to substitute, i.e. paths and domain name.

Then you just need to restart Apache:

service apache2 restart

And you should be good to go! :)