The high protein feed is only required during the first few rapid growth months and can be tapered down to the same 16% protein you feed your laying chickens for adult turkeys. The one issue that may exist is that layer rations have much higher calcium than a pet tom or hen out of season need. It might eventually cause problems but I am not sure.
If I could justify getting a custom blend I would get a layer ration with 18% protein. I effectively do that by blending different feeds and supplementing actively laying turkeys with extra Oyster shell in their feed. My chickens do just fine on 16% and Oyster shell available if they want it.