Probably somebody has already thought of this, but does your board have the capacity to cue sound while recording other sounds?
I notice a lot of "in the room, out of the room, covering ears" business, and if you just have people who aren't in the conversation keep their headphones on and switch the headphones to the cue channel, while running a line on the board with some music on the same cue channel, while Sark and his partner have a short 'phones-off conversation, it would make everything a bit more... elegant.
This is clear in my head but hard to put into words -- we used to be able to do this in radio, where I could have a song playing on-air, but switch the headphones to Cue, certain board channels to the Cue channel, and have completely different sound being listened to on the headphones than the sound we were broadcasting (in your case, recording).
Obviously not great for prolonged absences, but for a "hey Sark can I ask you something in private" sort of situation, like both Brian and Gerry found themselves in in today's ep, it could be a good answer to speed things along.