I am not sure that the conventional Buddhist notion of there not being a self really works. It seems like a doctrine that lacks a good reason. The doctrine (or perhaps more like a dogma?) appears to be more a consequence of another concept rather than having sounds reasons of its own. At a higher level of conceptual priority is the excellent idea that the basic ethic of any religion or philosophy of life should be the reduction of suffering. I fully agree with this aspect of Buddhism. But it then gets developed into the objective of the elimination of all suffering – hence the concept of Nirvana as a place, or time where suffering no longer exists.
But if Buddhism is wedded to the idea of the possible elimination of all suffering – and that suffering is caused by the self or ego’s clinging and attachment – then eliminating suffering necessitates the elimination of the self. So the concept of the elimination of the self is not particularly driven by empirical observation and psychological argument but by the religious or spiritual necessity of contemplating the possibility of eliminating all suffering.
We might be a whole lot better off if we were to redefine the purpose of Buddhism as being not the elimination of all suffering but the elimination of all unnecessary suffering. This would then eliminate the need to call for the elimination of the self and release it from what feels like outdated metaphysical claims.