Who sang the Cole Porter songs in the 1972 film "Sleuth"?

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Show notes:

• Sleuth (Wikipedia)
• Sleuth (IMDb)
• The Sleuth Saga Carries On (Reddit)
• The scene in question (YouTube)
• Cole Porter sings "Anything Goes" (YouTube)
• Thread on the Soundtrack Collector forum
• Massive thread on the IMDb 2.1 forum
• "One More Kiss, Dear" (YouTube)
• A page of the Sleuth cue sheet