I'm not sure what schedules look like these days but depending on the time of your flight and the current VS schedule, the Clubhouse may not even be open when your layover starts, so Centurion to Clubhouse may be necessary anyway. Remember to have your inbound boarding pass ready since you wouldn't be allowed into the Centurion lounge that long before your flight if you were originating in NY.

The JFK Centurion lounge has some nice nooks and even little enclosed rooms that are perfect for taking calls with some privacy, so that would work well (IIRC there are a couple of "phone booth" type spots that would be a little claustrophobic to hang out in for long periods of time, but I think there is also a slightly larger little room, with a door that can close, on the upper level on the side opposite from where the food is). I can't really think of anywhere at the JFK Clubhouse that would be equally good for privacy, so I would probably err on the side of staying at the Centurion if you have calls to be on.