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But each time, what it "was" did get "ruined" ... at least enough to change it into something different.

It's like the old koan about a radio: if you replace the speakers, then the housing, then the circuitry, then the controls, is it the same radio?

Koan about the radio?! Try nearly 2000 years old, also known as the Ship of Theseus (https://en.wikipedia.org/wiki/Ship_of_Theseus).

If you replace the object in the analogy is the thought experiment still the same?

Yeah, it pretty much is.