"my brain knows that he wants go home" instead of "I want to go home".

I'll admit to using that framing sometimes, but mostly for amusement. In fact, it doesn't solve the problem, as now you have to define continuity/similarity for "my brain" - why is it considered the same thing over subsequent seconds/days/configurations?

I didn't mean to say (and don't think) that we shouldn't continue to use the colloquial "me" in most of our conversations, when we don't really need a clear definition and aren't considering edge-cases or bizarre situations like awareness of other timelines. It's absolutely a convenient, if fuzzy and approximate, set of concepts.

I just meant that in the cases where we DO want to analyze boundaries and unusual situations, we should recognize the fuzziness and multiplicity of concepts embedded in the common usage, and separate them out before trying to use them.