Ok, I set this up for relay and it looks like it is working correctly now. I typically will set internal systems to use relay so thinking back I was wondering why I didn't do this originally.
After I initially set the IP and port under the SMTP settings, I saved the settings and it said successful. I then went to diagnostics to test it. I selected the from address, put in my email address in the "To" field and clicked Send Message. The web page just flashed and I didn't receive anything. There was no error message displayed so I wasn't sure at first what the issue was.
For those who may not know, you have to put something in the "Message" section as well in order for it to send an email. I am thinking that is why I changed to TLS for authentication instead of just sending to our relay.
Anyway, now it is working so thanks Kevin for the assistance!