This is all fascinating! I do appreciate your thoughts as an historian, too--thank you. It's become a quagmire to peer into the past. But you are asking good questions!
I've recently completed a children's novel set in Cheapside, London in the year 1526. In my research for children's games, I used this painting--link below . (A website with which you can examine closely--what a treat!) My characters played knucklebones, yes!
But it does appear that both girls and boys are indeed playing together! (I've made it a tiny url)