I'll usually go by shorthand, for one thing.
So, with your Higurashi example, I just call it... Higurashi. If I want to refer
specifically to the 2nd season alone, I'll call it "Higurashi Kai". If I want to refer
specifically to the 1st season alone, I'll call it "Higurashi's 1st Season". Yes, writing all that out is easier to me than remembering all those littler particles in Higurashi's title.
But on those occasions when I can't really dismiss the particles (such as with Shinsekai Yori), my personal rule is 'if the particle is 3 or more letters long, it gets capitalized; less than 3 letters long, it doesn't get capitalized'.
My biggest problem with anime title names is wondering at times how to handle those sometimes pesky exclamation marks. Writing "K-On!!" in the middle of a sentence kind of looks wrong to me (i.e. having exclamation marks in the middle of a sentence). At the same time, ending off a sentence with "K-On!!" makes it seem like I'm really shouting the entire sentence that "K-On" is in, lol. I still haven't made up my mind as to the best way to refer to "Little Busters!".