Update on OpenDNS and USF Mail
I have traced the mail problem down to the USF Mail server itself and whatever policy it has. I enabled SMTP logging in Thunderbird and was able to see the SMTP conversation Thunderbird was having with the server. It turned out that my Thunderbird is giving the USF mail server (and only the USF mail server) ELHO [127.0.0.1]. I changed some settings around in Thunderbird and got it to send ELHO [10.0.22.10] like it should, but after sending one message fine with that, I continued to get the blacklisted message.
As far as I can tell, the USF mail server will add internal IP addresses to its blacklist if the client saying ELHO with an internal IP address is coming from an external USF address. This may be due to their policy of no unauthorized switches, hubs, or routers within their network policy. I will continue to resort to using Tor to send my USF e-mail.