I have not read all of these, so I may be repeating, but I had a similar difficulty during my first teaching job (one hour away, stayed until 8:00 at night, a walking zombie all the time, etc.). It does get better, but you need to take care of yourself (and your job) in the meantime.
I really like having students grade their own work. It doesn't always work at the beginning of the year when they're first learning the ropes, but I just had my 7th graders grade almost their entire writing assignment. I just graded one paragraph. Also, is it possible for you to only grade parts of their essays? On my first set of essays, I only graded their Thesis and Body Paragraph 1. It goes by a lot faster, and they still get some good, solid feedback. Oh, and I devised a grading system for their rough drafts that consists entirely of highlighting. They have to figure out using my chart what they need to change on each section. It engages them, and it makes grading so much easier for me!
As for the little assignments, I have the students place the assignment on their desks when they're doing their start-up activity, and I go around with my seating chart and check them off. It's also a good way to get some face-time and check with students individually who need some feedback or who need some prompting to get their work turned in on time.
Hang in there! It's hard to be motivated, but you just have to do it! Make SMART goals that are measurable, like KateL said earlier. You can stay a bit after school, but just say you have to grade 10 essays (or five, or three).
Also, I used to listen to books on CDof the novels/plays I was teaching on my commute to save time having to read them at home. If that's an option for you, I strongly suggest it.
Long post short, anything that can put more on the students and less stress on you (to a point, obviously) can be very helpful in making them independent learners. Find your balance. It sounds like you're doing well with everything else; grading is just a constant challenge.