IMO, the most significant increase in turkey predation of the past decade has come from raptors.
I don't know of any legal way to eliminate or reduce their numbers.
Not only are the raptor numbers continuing to increase, but they seem to be evolving to more specifically hunt turkey, and get more efficient at doing it. The Cooper's hawk is particularly preying on young poults, the red-tails are getting the larger poults, the owls are getting all ages, and the bald eagle is more specifically targeting strutting Toms (or any turkeys caught out in a field).
I also think the turkey population declines may have some other yet over-looked or unrecognized factors, just like the now near extinct bobwhite quail. Whatever is going on, it's not just about habitat, nesting success, and predation. I've seen too many very large acreage areas (many square miles) develop improved habitat for both quail and turkeys, yet their populations fail to thrive.
I also don't think the declines I've seen in Stewart Co have anything to do with chicken houses or chicken litter. Maybe in some areas, more chickens equates to more robust raptor populations?