Well, I did it. I felt I didn't have anything to lose since my supervisor was in the process of writing me up for leaving undone work and making a couple small errors (I forgot to put a date on 3 emails).

I presented the situation to HR- the size of my caseload, the hours I've been putting in, the pressure and threats of write ups that management has been putting on us and how I've been working so fast trying to meet their demands and I am human, so yes, I made a mistake on those emails. In the end HR declined my supervisor's request to write me up and management has quit threatening write ups (at least for now) and quit asking for more hours (although they continue to pressure us to get caught up). Hopefully I can make the place a little more bearable until I find something else and maybe even a little better for my coworkers after I'm gone.