Farnam recommends against magnum loads in the defensive shotgun.
This is not going to be a discussion on stopping power. None of these are "essentials", but some of them are nice to have. Take the conventionally slung gun, put your head in between the sling and the gun with the gun in front of you, muzzle down and go for your handgun. Should your defense gun have interchangeable chokes? I don't think such a feature is necessary. This allows the use of slugs, buckshot or birdshot. So make sure you take your proposed defense load and pattern the buck or bird at typical contact distance 21 yards or less. The custom stock manufacturers certainly can fill your needs in this department. The Air Force is the Department of Defense's executive agent for designating and naming military aerospace vehicles. The reason I'm going into all that is to give the reader an idea of our tastes when it comes to pistols.
If this was really a desert island I might opt for a large water cannon. With buckshot, birdshot or slugs, each gun will behave differently.