Swarms will either stay, or they will go. A frame of emerging brood would be a nice shot in the arm, IF you have resources to potentially sacrifice. I have hived swarms about that size, and with a nice queen, many have lived and thrived (and some have not). I have never left the queen caged beyond the first night. Release her, and let the bees decide the rest. I have also seen swarms leave the box and leave the queen behind. Bees are bees...Good luck!