Success!
I removed the extra domain, and while that didn't fix the problem, it gave me a new error (SAML 2.0 token...), and the imsTrace.log stopped doing it's crazy growth, which allowed me to actually look at it.
After a bit of research, I added both domains to the 'Append these DNS suffixes' in the network card configuration, and I can now login successfully through the vSphere client and the web client.
Thanks,
Brian