At last the A7rIII is in Stock at BHphoto too. It is in Sotkc since yesterday at KenmoreCamera and at Adorama (free overnight shipment).
Still, I am a bit surprised to see that the 24-105mm FE is nowhere near in Stock at Bhphoto, Amazon and Adorama. Today Amazon updated the shipment status and says the lens will ship within 1-2 months. Seems like orders are really high!
Reminder: You can win a 24-105mm FE lens on SAR (read here).