 IMHO
If it's a recording session and not a concert...why not mic them multiple ways? Do your omni mic thing, but also stick a pair of mics in the piano and put something closeer in to the vocalist. Listen back in your studio and then you can learn how that omni mic technique sounds but have a backup if you don't like it. I'm a huge fan of having options for the mix!
Have fun with it.
Rob
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