For my third-round choice I'm going to go with
The Big Lebowski (1998).
This movie has everything - a main character named simply The Dude, bowling, a ringer of whites, nihilists ("Say what you like about the tenets of National Socialism, Dude, at least it's an
ethos"), a segment from Mussorgsky's Pictures at an Exhibition, and a rug that really ties it all together.
The Big Lebowski has a plot complicated enough to stand up to (require, really) multiple viewings, and pretty much every time I watch this movie I catch something subtle I hadn't noticed before. Perfect for my island.
Official trailer below: