This is a good article on how to think about approaching the HR challenges, I've been writing about in the Mindful Firing series:

https://www.forbes.com/sites/lizryan/2017/05/13/how-to-get-rid-of-a-problem-employee/#71d6ecde6717

It comes from a little brighter place, in the sense that it is about approaching your culture from a non-firing perspective (at least it shouldn't be your first step) and making changes to corporate culture.

I very much agree with this.

This is good to read to keep you focused on problem solving and solutions. Those solutions are out there in many cases.