One thing I will mention is that your turkey WILL eat the same number of calories to meet his daily energy (not nutrient) need. So when we switch from higher protein we MIGHT get higher carbs instead... Different phases of life do have different requirements.
I basically use Purina Flock Raiser... which is 20% protein... and has worked very well for several years... (not for young poults) but yes for turkeys, chickens and duck... Do you have any other birds... or just these 2?
Interestingly.. I often see LOWER protein GAME bird... chows...
@R2elk can you please share your thoughts on these products and would you still go with a chicken feed if you have NO chickens?
Like this "maintenance" one..
https://www.purinamills.com/game-bird-feed/products/detail/purina-game-bird-maintenance-chow
Or the "flight conditioner"...
https://www.purinamills.com/game-bird-feed/products/detail/purina-game-bird-flight-conditioner
Would something like this address the OP's concern (IF confirmed)... Although I stated protein and carbs have the same energy content... maybe something higher in fiber has a different impact??