Cannot access Apache 2 virtual host on localhost

I originally set my web root in /etc/apache2/sites-available/000-default.conf to point to /home/me/www. Due to the requirements of a new project, I need to be able to set /home/me/www/vendor/www as its own virtual host as any local directory cruft in the request stemming from localhost/blah/blah/blah will currently cause it to fail (the site is pretty horrible, codewise, which is why I've been contracted to work on it).

I have the following config file in my /etc/apache2/sites-available -

project2.com.conf:

<VirtualHost *:80>
    ServerAdmin webmaster@localhost
    ServerName project2
    ServerAlias localcopy
    ServerRoot /home/me/www/vendor/www/
    DocumentRoot /home/me/www/vendor/www/
    <Directory /home/me/www/vendor/www>
        Header set Access-Control-Allow-Origin "*" 
            Options Indexes FollowSymLinks MultiViews
            AllowOverride All
        Require all granted
    </Directory>

    # Available loglevels: trace8, ..., trace1, debug, info, notice, warn,
    # error, crit, alert, emerg.
    # It is also possible to configure the loglevel for particular
    # modules, e.g.

    #LogLevel info ssl:warn

    ErrorLog ${APACHE_LOG_DIR}/error.log
    CustomLog ${APACHE_LOG_DIR}/access.log combined
</VirtualHost>

# vim: syntax=apache ts=4 sw=4 sts=4 sr noet

I also have the following entry in my /etc/hosts file:

127.0.0.1   localhost
127.0.1.1   Shevat
127.0.1.2   project2.com

# The following lines are desirable for IPv6 capable hosts
::1     ip6-localhost ip6-loopback
fe00::0 ip6-localnet
ff00::0 ip6-mcastprefix
ff02::1 ip6-allnodes
ff02::2 ip6-allrouters

However, when I attempt to access project2.com through my browser, it displays the contents of the /home/me/www directory instead because, like I said above, I set that as my global web root in /etc/apache2/sites-available/000-default.conf.

Is there a way to override the global web root/virtual host settings in this instance so project2.com is accessed properly?