For a good (motivational) read about the definition of grit, who's got it, and why it matters, I recommend Angela Duckworth [link]http://angeladuckworth.com/
The standard advice while doing anything that is that long and stressful, is to try and not quit the next 5 minutes at one time.
But even in the case of Hell week, the worst part is the first 2.5 days. If you can make it till there, you finish the week. The instructors also don't push you to the point of the falling to total exhaustion, they know, if they have seen you hold on for half the time, you will get the remaining done easily.
If I know it's a trick enough to try it, then I know it's a trick enough to see through it.
This isn't "outsmarting" yourself, its simply getting past the hardest part. It's difficult to "get off the couch" if I think I'm committing myself to running 10 miles. But I can easily get off the couch to run for 5 minutes. After 5 minutes, I can quit, or keep going. Sometimes I quit, sometimes I keep going.
Something that has worked for me is committing myself to a short amount time doing the thing I don't want to do. I'll tell myself "after 5 minutes, if I still don't want to do this then I'll stop". Nearly always once I start washing the dishes or start a run, I'm happy to finish.