My comments are going to be about opposite of Ducklover1. If you offer oyster shell on the side, the feed does not have to have any additional calcium. The ones that need the calcium for the egg shells will get that from the oyster shell. The others don't need it.
Last time I checked, 22% protein level in the Gamebird starter/grower is higher that the 16% protein in regular Layer so it will support their protein need for laying. I'm not familair with that specific brand, but I'm assuming the amino acids added, Lysine and Methionine, are about the same. Somewhere around 0.7 to 1.0 for Lysine and 0.25 to 0.4 for Methionine. It should be on the label.
I think you are OK with either feed. At those ages, they don't really need the higher protein stuff, but it won't hurt them. With your mix of birds, my preference would be around a 20% protein feed, but since I think you are raising them to be a lying flock, not a meat and laying flock, either should be OK. If you are raising some of them for meat, I'd go with the higher protein choice. With the 15% protein feed, your egg size might drop a little, but it should not be a drastic drop in size. The "recommendations" are for maximum efficency in growth and development related to cost and production. Poultry are pretty forgiving in their diet as long as you don't go to extremes. I don't consider either of those extremes.