Well, Microsoft Tech support was able to help me. :)
Basically, we had disabled the RC2 and RC4 ciphers to pass a PCI Compliance audit.
Something must have changed yesterday at UPS where they no longer accepted DES or DES3 ciphers on the server that our systems kept hitting.
The solution was to re-enable the RC4 128/128 cipher and restart Internet Explorer. That allowed me to get to the UPS.com site via https.
Once I verified that, I had to reset the IIS worker process for my websites and they were able to successfully calculate shipping charges again.
Just as a note - Fiirefox must handle SSL differently, the system settings didn't seem to affect it's access of the website, while IIS, WFETCH and Internet Explorer all were working under those system-wide registry settings.
Thanks for the suggestions!