We have found that the nestbox the turkeys adored the most is the one that we built around them when they went broody.
Chicken wire, old scrap lumber, and something to weigh down the top. Once you find where she has gone broody then measure out a decent cage (if you don't have one on hand) and lay it over her and the nest so that she is away from any of the sides. Weigh it down so nothing can topple it over and put cinder blocks (or something heavy) around the base so nothing will dig under. A folded out wire base also works well so that animals that are digging hit the wire and assume it's a lost cause.
Besides keeping them locked up during the breeding season, that is the only way we have found to keep them broody, on the nest, and safe from predators.
Inside the pens when we do lock them up we provide tires full of straw for them to use as nests. Our turkeys and geese love them for laying. We can make a shelter over the tire if we want someone to go broody in there after enough eggs have been laid. Mostly that is used for our geese.