Welcome to reality! Don't work outside of your contract, because, as you've clearly pointed out, you're giving away labor for nothing.

To answer your question: I don't grade everything (actually, most of the work the students do doesn't get graded, because it's part of the learning process). I only grade evidence of learning. Anything I don't finish doesn't get done until the next day. Now, to be fair, I have more than three decades of time put into this little party, so it's a lot easier for me now. I have always done this (well, starting with year #2 anyway). Best advice I ever got from my mentor.

Realistically, it requires a very pragmatic look at this job - we're not saviors; we're not going to change the world. We're there to form relationships (which is what you should be doing in class), and teach our content. If you maintain the non-romantacized view of the job, it's a little easier. There will always be those that criticize you for not "going above and beyond" - they don't last in this job.