Socialism

Yeah this. Doesn't particularly if it's neuron by neuron or larger scale repairs. So long as not too much is replaced at once, and everything is backed up in software before very the switch, then I'd still be mostly me. I can't imagine the changes wouldn't change my personality, capabilities, etc, but I feel like I'd still be me so long as nothing fucks up in the process. Much better than whole brain backup/cloning, even with neuron-by-neuron copy+destruction.

EDIT: where it gets sketchy is handling conscious (especially internal monologue) and nearly conscious sections. Those would need to be replaced at a slow rate IMO.