Postfix is getting "TLS Is required, but was not offered by host"
With the help of everyone at serverfault, I dug deeper into the issue and found that my host is indeed blocking TLS. After speaking with my host and being told they do NOT filter SMTP, they finally admitted to filtering SMTP.
I resolved this issue by setting up a VPS relay server at another host. My primary server now sends mail via the relay on a non-standard port. With this setup, I am able to send secure emails without my hosting filtering them.
Thank you again for the help.