It's been a year, but I wanted to post an update. I finally was able to connect and use the Automatic Update Package!
The settings I used are different from what FileZilla requires. I couldn't connect via automatic update using my normal username and password that I use within FileZilla.
I went into my cpanel/FTP Accounts and created a new FTP user account with access to the public_html folder. I had to use ftp in front of my domain name and had to use @mydomain.com after the user name as follows:
FTP Username: firstname.lastname@example.org
FTP Server: ftp.mydomain.com
It worked perfectly! I used to dread doing forum updates but now it'll be easier to keep it up.