Late US calls in a 2BHK with a 1 month old asleep next door

My calls with the US team start at 8.30 pm and sometimes run past midnight. Before the baby I took them from the second bedroom. That room is now where my partner and our daughter sleep, because it is quieter and cooler. The living room shares a wall with it, and even with a headset my voice carries. I have tried the balcony, which works until it rains or the neighbours' dog joins the meeting. For those who work late calls from a small flat with a newborn, where did you end up taking them? Did anything help with the sound, or did you end up shifting the hours?