I don't know. I suppose that would feel a lot like what we feel in our current state, since, as you point out, memory recall isn't flawless. I guess we are always shifting identities; re-engaging with our memories, preserved at whatever level of fidelity they may be, in each present moment.

The question of "when we become a new person" seems to be asking for something that may not be possible to define or answer. It feels like the only answer that makes sense is that we are a completely new person perpetually, and that static identity, of any kind, is only a (pretty damn persistent) illusion.