Turkeys are wanderers. They just are. My Bourbon Reds are home much of the time, but if it is springtime (or nesting season) where you live, they will range farther when they are looking to make a nest. Mine behave differently when they are looking to nest, than when they are just foraging for grass. They do weird things like look around a lot to see who is following them, and they seem much more focused, like you're describing.
Mine free-range every day and sleep in a tree in my yard. As they grew from chicks to adults, they wandered slightly further each day. I make sure to have food and water for them at my barn and I feed them treats regularly so they know where home is. However, they typically will wander around the yard, the buildings and some of their favorite hangouts, like out in the pasture, and down the driveway -- but not as far as the road. They spend 70 percent of their time here at my barn and maybe 30 percent of their time wandering. However, mine almost never go further than about 500 yards. The exception to this is when they want to lay a nest of eggs. Or, in my case, when they discovered a market across the street with lots of treats and shiny things to look at. (they would sneak over to the market at 6 a.m. and be back at 7:30 when I went outside to feed them so I didn't know. I found out when the market vendor chased them into the creek on a 10 degree freezing day and they were covered in icicles and shivering when I woke up. After that, I locked them up on market days and that worked to keep them away).
Best case scenario, is if they are laying a nest -- to pen them up (one per cage is best so they don't fight over the nest and crack the eggs). They become very focused on nesting, though it may take 2 weeks for a nest to have enough eggs for them to set on it.
If they lay a nest elsewhere, they usually find obscure spots, often in tall grasses or brush or places where you can't find them, and possibly far away. They will return to that nest every day for 2-3 weeks and lay one egg. When they start setting, they will not return home and will sit on the nest for 28 days until the babies hatch (except for once a day if they need food and water they may run to your place in a hurry, then run back to nest which they do at my place). You can tell if they are nesting because they get very sneaky and try to "shake" the rest of the turkeys so they can have solitude.
If you have predators, the turkeys can get killed while setting on the nest -- which is why I recommend penning them up for nest setting. the poults may hatch but get eaten by hawks or predators or die of thirst if they can't get to water, so that's another reason not to let them hatch out in the open.
Once they establish a nest somewhere "out there" it can be very hard to find it! I've tried and only found the nest because the tom turkey is hanging around, or because I watched the turkeys behavior very closely and followed them to the nest.
By the way, your *girls* look exactly like mine!
Good luck! Enjoy them.
