The doctor is Takumi. We were made to think that the headless body was Takumi but it ended up being the 'ugly' conductor. So, our attention was diverted from his dead body. We have only witnessed his death on stage. We don't know what happened after with him. The most important evidence is that he retrieved the ring. Nobody knew that Takumi was going to propose to Naomi or that the ring was missing from the 'dead body'. Remember that the police came after the accident in the theatre, maybe he was saved by that detective.
The doctor is Takumi. We were made to think that the headless body was Takumi but it ended up being the 'ugly' conductor. So, our attention was diverted from his dead body. We have only witnessed his death on stage. We don't know what happened after with him. The most important evidence is that he retrieved the ring. Nobody knew that Takumi was going to propose to Naomi or that the ring was missing from the 'dead body'. Remember that the police came after the accident in the theatre, maybe he was saved by that detective.