Hi,
I am very ignorant about flying, but a little less about physiology. Imho, THE problem with recovering people is about pressure. Even around 4°C, there are some chimical processes. And many decaying processes involve gases* formation. The only way to recover bodies without inconvenients would be to pull them up very, very slowly to give time to gasses to dissolve. May be days, perhaps weeks: dive computers don't give time for this kind of depth!
*and perhaps even solids as methan ice, which will sublimate at low pressure.