The op is extremely certain that they have interpreted this law correctly, but the fact of the matter is that a case like the one you describe has never gone through US courts, so we do not know. We are likely to have a court case sometime in the next few years it seems, who knows how long it'll take to get an answer though.
There was a very important and similar case though where Bette Midler sued Ford over inappropriate use of "her" voice performed by an impersonator.
The context seems important in that case though. Ford had the impersonator sing a song that she herself released! (They had acquired copyright release for that part) So there's no reasonable claim that Bette Midler was not the one they were impersonating.
If you sang a song you wrote in a voice extremely similar to Drake's without mentioning Drake in any way, then that seems very different to me.
There was a very important and similar case though where Bette Midler sued Ford over inappropriate use of "her" voice performed by an impersonator.
https://en.m.wikipedia.org/wiki/Midler_v._Ford_Motor_Co.
The context seems important in that case though. Ford had the impersonator sing a song that she herself released! (They had acquired copyright release for that part) So there's no reasonable claim that Bette Midler was not the one they were impersonating.
If you sang a song you wrote in a voice extremely similar to Drake's without mentioning Drake in any way, then that seems very different to me.