Cosmic radiation would slowly cook the bodies over centuries, erasing any recoverable consciousness information still present, unless they are heavily shielded

Cosmic radiation would slowly cook the bodies over centuries, erasing any recoverable consciousness information still present, unless they are heavily shielded (Earth atmosphere provides ~10 ton/m^2 shielding for free), say, buried in a moon pole crater. People planning for immortality also would balk at the several % risk of rocket failure. A compromise would be to create a facility in an Antarctic plateau, where even in total failure temperatures wouldn't go beyond -30C (or -50C in winter).