Structural brain preservation (SBP) and classical cryonics are techniques aimed at preserving the human brain for potential future applications. Reluctant public discourse around these techniques may be explained with intuitive aversions identified by moral psychology. In the first part of the paper, we conjecture the existence of a self-sustaining cycle of moral condemnation of SBP and classical cryonics due to quick, affect-laden moral intuitions. In the second part, we propose an alternative framing of SBP and classical cryonics through a thought (...) experiment featuring a time machine metaphor called "Schrödinger’s chrono-cat", which might avoid triggering aversive moral intuitions and foster public discourse. We discuss the limitations of this framing and its consequences. (shrink)