I want to have slaves set as sub directories on my site (site.com/slave1, site.com/slave2, etc.) where site.com holds the main joomla installation. Right now, I get the custom Joomla 404 error for site.com/slave1, but the site comes up for site.com/multisites/slave1 even though both http://{site_url}/{site_id} and http://{site_url}/multisites/{site_id} are defined in the domain list.

Is there anyway for me to remove the /multisite from the URL?

The /multisites directory must exists on the disk because this is the place where JMS save all the website definitiion.

You can define only http://{site_url}/{site_id} and let the /multisites directory almost empty (not completly as JMS save its configuration in this directory).

What you can do is to ask deploying the slave site into the {root}/{site_id} directory that correspond to the domain http://{site_url}/{site_id}.
As JMS does not create the directory, you have to create the deploy directory before that you use it into JMS.

If you want completly deny all the access to the /multisites directory, you can add a ".htaccess" file with "deny from all".

In summary:
- Create a directory xxxx in you master website directory using FTP tool, SSH or other tool.
Go in JMS site manager
- Site ID = xxxx
- domain = http://{site_url}/{site_id}
- deploy directory = {root}/{site_id} : Remember that the directory must exists.

In the /site/multisites folder there are folders for all the slaves. Can I move those folders to the root, or do I have to leave them there in addition to creating the /site/slave1 folder?

NO you can NOT move.
As I told you, JMS save its own configuration in those directories.
All you can do is to deny the access to thoses directories with a ".htaccess".

Apply the procedure described and you will see that you will have a very limited number of files into the /multisites/xxxx directories.

When I use those steps, the site.com/slave1 now comes up, but with the initial Joomla installation guide instead of the slave site.

Exact.
The sample that I have given to you use the tutorial step 9 procedure with another deploy directory.

If you want to replicate a website, you have to create a website template and select it.
See sample in the tutorial step 13 that show how to use website template fro the front-end. This procedure can also be used in the back-end.