I suspect that asking your parents if you could be more frugal and they would donate the difference would just strain your relationship to little gain.

This is why I never tried it. When choosing which college to go to, I did ask whether going to the vastly cheaper of two options and donating the difference was an option, and was told it wasn't, and I could tell that similar suggestions along those lines wouldn't go over well. (In retrospect, it was good they kept me from doing unusual things like that, and that I'm so influenced by social norms - taking beliefs seriously while still a stupid kid in other ways is dangerous.)