Tentatively Christian; looking for a reasonable discussion

[Neo-Scholastic]

They are basically the same problem. Anyone, but Heraclitus, can see that from cradle to grave, Joe is still Joe. And anyone, except Parmenides, can see that Joe has changed in material composition, size shape, and capacities. I wish there was a philosophical tradition that could somehow resolve this dilemma. Hmmmmm....

...Joe may have changed in material composition, but he has not done so entirely, all at once. Joe changes gradually over time, and since "Joe," as an identity,exists as a process going on within Joe's brain, that process can persist regardless of how many physical things change...

Maybe you didn't catch someone else's reference to Theseus's boat earlier or Pizz-atheist who further observed that when the contents of consciousness change then so also does any mental basis for a sense of self. Your proposed 'solution' only disguises the problem and doesn't answer how the identity is preserved throughout changes.