"His voice is unique, and is one of the best ever." I'd say.
As it stands your sentence suggests his voice belongs to a number of unique voices.

weil "einzigartiger" gibt es ja nicht.

'einzigartigsten' übrigens auch nicht. Wenn etwas einzigartig ist, gibt es kein zweites davon. Das kann man nicht steigern.

I would avoid 'unique' - an over-used word, and would say:
He has one of the most beautiful and individual voices in music

Agree; every person in the world has a unique voice - like faces, and our bodies for that matter.

Even identical twins can't be really identical presumably - exactly the same number of cells e.g.? :-)

It doesn't jar like "more unique" etc., but should one say "most...individual..."?

most outstanding ?

Another option, just for comparison, might be 'distinctive,' but I like 'individual' here too.

Or perhaps 'unusual,' if he has some strange quality to his voice. (High falsetto or countertenor; Tiny Tim; Leonard Cohen ...)