"Your ideas fall apart in a disaster scenario, like when there aren't enough lifeboats on a sinking ship, or in an airplane disaster without enough parachutes, or the Donner Party choosing cannibalism to avoid starvation!"
In each case, the issue is resolved with clear property rights and contracts. If you are sailing on a ship, you want to know their lifeboat and flotation device situation. If you are flying in an airplane, you should know the parachute policy. In a free society, someone providing a service is liable for any injury or death and is obligated to take reasonable precautions. As a consumer, it is your responsibility to assess risks and make your own cost/benefit analysis. In circumstances where such matters may be outside your control, resource distribution is the responsibility of the resource owner, or a case of homesteading when there is no owner.
In situation where the options are choosing to suffer either death or injury versus committing a crime, the party committing the crime acknowledges the crime, and must be willing to face the consequences upon a return to normalcy. Whether it is a matter of simple trespass, such as running through private property to avoid an attacker, or an extreme situation such as choosing cannibalism over starvation, the same rule holds true. (LT)
In the normal conditions of existence, man has to choose his goals, project them in time, pursue them and achieve them by his own effort. He cannot do it if his goals are at the mercy of and must be sacrificed to any misfortune happening to others. He cannot live his life by the guidance of rules applicable only to conditions under which human survival is impossible. The principle that one should help men in an emergency cannot be extended to regard all human suffering as an emergency and to turn the misfortune of some into a first mortgage on the lives of others. - Ayn Rand, The Ethics of Emergencies
See also:
Rothbard's The Ethics of Liberty, chapter 20, "Lifeboat Situations".
Objectivism 101: Ethics of Emergencies