HAHA! IT WORKS!
Alright, so for anyone in the future who comes across this issue, Naka's stuff was correct. I will put the step-by-step below for easy following...
1.) Download the seafdav server from here, and the seafobj files from here.
2.) Extract the seafdav files into a folder in the root directory (such as c:\seafdav)
3.) Copy the files from C:\Seafile\seafile\lib (or wherever your seafile install directory was) into C:\Python27\Lib.
4.) Copy the files from the seafobj into C:\Python27\Lib\site-packages
5.) Set your environment variables as follows:
CCNET_CONF_PATH = 'C:\seafile-server\ccnet'
SEAFILE_CONF_DIR = 'C:\seafile-server\seafile-data'
SEAFILE_CENTRAL_CONF_DIR = 'C:\seafile-server\conf'
6.) Create a file called "seafile.ini" in your C:\seafile-server\ccnet folder, and in it, put the path to your data directory (such as c:\seafile-server\seafile-data).
7.) Execute the server by opening a command prompt, navigating to c:\seafdav, and running the following:
python -m wsgidav.server.run_server -H 0.0.0.0
This will make it publically accessable - and it's what worked for me. Browsers won't show anything, but connecting with a WebDAV client (such as WPS Office on a Kindle Fire) will navigate just fine.
Edit: For those who want to run this as a service, I recommend NSSM. When installing, just point it to your python.exe file, set the startup directory to be c:\seafdav, and the parameters will be "-m wsgidav.server.run_server -H 0.0.0.0".