I think the barbecue is a wise and practical choice. The King and Queen will be meeting a large number of people and there's still HM's cancer diagnosis and the danger of picking up a respiratory infection or some infection. There's a wide open airy venue for HM.
Oh, I hope the King doesn't go with your suggestion Nellie Maybe casual khaki or blue slacks with a lightweight button down shirt and casual jacket? I don't know, the King can be pretty set in his way with clothing.