Extensions of the Standard Model (SM) scalar sector featured in radiative neutrino mass models possess the ingredients for exotic thermal histories and rich possibilities for beyond SM physics. In this talk, we will explore the possibility of early Universe non-restoration of the $U_Y(1)$ gauge symmetry in the Zee-Babu neutrino mass generation model and the ways in which this phenomenology can be harnessed in mechanisms of baryo- and leptogenesis. We will find that subtleties in the treatment of finite-temperature perturbation theory play a decisive role in mapping out the parameter space of phenomenological interest. Moreover, we will re-encounter many of the pitfalls, lessons and open questions of past research on high-temperature inverse symmetry breaking and symmetry non-restoration. The highlight of the talk will be the outline of a novel baryon asymmetry generating mechanism which crucially relies on the high-temperature $U_Y(1)$ breaking phase and the exotic phenomenology of charge-breaking SM lepton masses therein.