Based on your set of ideas, I went a little bit further than I have before and was able to get back to a state where I am able to successfully access any of our environments.
I started with the test of removing besclient. At first, no resolution. Tried removing the remnants still in the BESClient program files directory. Still no resolution. Uninstalled the bes console, removed remnants of this as well, then reinstalled console.
Something to do with this mixture of actions allowed me to login again.
Not nearly as intrusive as re-imaging, but also way bigger of a hammer than I would think needed to be used.
Going to continue poking around at this whenever it rears it’s head again.