Cost Element Type need to be re categorized for the existing defined cost elements

Summary:

We have cost elements configured with an incorrect Cost Element Type (e.g., typed as Material Overhead, when the underlying calculation logic is actually labor/operation-driven and would be more correctly typed as Overhead). Business requirement is that the Cost Element Name must remain unchanged as the best case— we can't simply retire it and stand up a replacement under a new name.

There are live financial transaction and item costs with these cost elements in production environment.
Any use cases or similar experiences to be shared?

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What we've found so far: