I haven't bought the DVD, fearing I'd be tempted to overwatch and become desensitized. I hadn't seen it since it left theaters, so about two months. Then I rented it last week and watched it twice, beginning to end, because it was a two-day rental. Later, I realized my kids would be getting out of school in a couple of weeks, after which my viewing would be curtailed, so I rented it again yesterday and watched it once, beginning to end but FFing through a few parts because I was short on time. It has since become an eight-day rental, so I have it until next Friday and may watch it once again before returning it. (Always alone -- I've only seen the movie one time with someone else.)
I might be tempted to skip around more except that I a) agree that you lose impact that way, b) have lost my remote and c) watched some of the best parts time and time again on YouTube. Still, not surprisingly they are MUCH more intense on the DVD. Sometimes I do reverse and watch parts twice.
But rt, I think you should also ask how many times people saw it in the theater. I saw it "only" seven times there. If that number were different, it might affect how often I'd watch the DVD. Also rt, you didn't say how many times YOU have watched your DVD.
You expressed this really beautifully (though I myself CAN'T look away):
I find myself, nearly each time I see this scene, looking away from the screen when Heath breaks into his "I'm nothing" line. It gives me chills actually, the level of commitment he has in that scene and I feel as though I am eavesdropping on the private pain of another human being, and like it's something I should not see. It also overwhelms me from an acting standpoint and I guess it just hurts to watch it. Never once seen that moment without a few tears of my own. That scene is unparallled in terms of writing and acting. It just can't get better than that.
As for your other question, I'm sorry but I can't think of any. Either Sophie's Choice or Schindler's List might be a candidate, and I would hate to think I wasn't deeply moved by the Holocaust, but I saw those so long ago I can't remember my emotional reaction very well. I can tell you I haven't been tempted to watch any movie 10 times since I was a kid.