Just on a mad one here, but what if the Richat structure (About 11000 years ago) became an outlet for the remains of the Tethys sea? If there are or were massive aquifers underneath the Sahara - the remains of the Tethys sea, could the African humidity period have been caused by the up welling of gases from this area due to the pressure build up by the higher ground level sitting to the east?
Go easy. I'm not a geologist. (-;