I take similar trips every year coming back from Europe. I usually fly from the continent to LHR, then from LHR to LAX.
I just pretend it's a very long day. I take my iPod, Kindle and a Sudoku book. Usually I load an interesting audio book in my iPod, so I can close my eyes and just listen.
And, yes, I always fly Coach. I am too cheap to pay for an upgrade.