Your second paragraph about sound mimickry, as far as I’m aware, is not accurate.

It is. The recording copyright is separate from the musical composition copyright. Here's the statute governing the rights to use a recording:

The exclusive rights of the owner of copyright in a sound recording under clauses (1) and (2) of section 106 do not extend to the making or duplication of another sound recording that consists entirely of an independent fixation of other sounds, even though such sounds imitate or simulate those in the copyrighted sound recording.

So if I want to go record a version of "I Will Always Love You" that mimics and is inspired by Whitney Houston's performance, I actually only owe compensation to the owner of the musical composition copyright, Dolly Parton. Even if I manage to make it sound just like Whitney Houston, her estate doesn't hold any rights to anything other than the actual sounds actually captured in that recording.