Well, I would take the backstraps, too. Who is going to stop you? You are still donating 90% of the meat to the needy, even if you do keep the best cuts for yourself.
Don't bind the mouths of the bowmen who tread the grain, ah, er, harvest the deer, or something to that effect. :-)
This guy saying no one likes to shoot deer I can come up with millions of people every fall that get great enjoyment from shooting and killing deer.