Turkey feed that contains how much protein? Too much protein can cause gout and kidney failure. I would NOT feed more than 25% to chickens and probably not even that long term. The turkey feed they have here is 26-30%. It's true the extra protein will be processed by the kidneys (hence possible issues) and then excreted as super smelly waste. And fat hens have a harder time laying. Depending on your breeds, a little extra protein is preferred and even been shown to give better hatch rates in breeding birds, which to me does say better nutrition for my family. Many show breeders also use a "higher" protein feed because feathers are made of 90% protein and the amino acids it contains. So they know it gives them better overall feather growth and showing ability. But they mean higher than the 16% that is in layer. Not double!
If the started you fed is unmedicated and affordable, I would feed that before going with the turkey feed.
My flock does get Purina flock raise 20% protein, because I have mixed ages and genders. It $20 for 50# if I buy local and $17 if I buy when we go to the city. I also have turkey "starter" for $18/50# at 26% protein, but it's only pellets and not crumbles and crushing is a pain for chicks. I do sometimes mix the 2 and aim for 23% protein because I do breed/hatch and all of my birds are dual purpose.
Here is one link I use. It has a misprint that say 5-17% and should say 15-17%...
http://ucanr.edu/sites/poultry/files/186894.pdf
As far as chick starter goes.. keeping chicks free of cocci is easy by simply keeping their water poo free and their bedding dry. It can be harder with large broods, but very doable. No need for medicated even if that's what the feed store insists. 
