I think you led me to the problem. I updated the original comment, but I think the issue was that v4l2loopback was being loaded without any options and screwing me up, so rmmod ing it and reloading it seems to help
/etc/modprobe.d/v4l2loopback.conf:
options v4l2loopback devices=1 video_nr=10 card_label="OBS Cam" exclusive_caps=1
/etc/modules-load.d/v4l2loopback.conf: v4l2loopback
Working flawlessly so far in Hangouts and Zoom using OBS Studio and the obs-v4lsink plugin.