Sorry, I don't have the reference in front of me, but did you change the default Audio settings in OBS to match FB's recommendations? both in Sampling Rate (44.1kHz vs 48) and Audio bitrate (128 vs default 160), iirc...
No idea if this is accurate, but I read recently a recommendation to change to Advanced (vs Simple) on Settings-> Output and change the Keyframe interval to 2 (.. no idea if that would impact audio sync as well)
