It all depends on the the weather your location you don't show any idea of were in the world you live so its even harder to guess for your situation.
From what I have learned Spring is the Season to start for the year laying and it stops for most in May in my area.
With any birds when they go Broody the egg laying stops so when you allow eggs to stay in place for the Hen to set on them she is done laying eggs for the most part that season.
You maybe able to get a late lay of eggs in the fall at least I have seen people report late in the year Hens Laying.
Its great that you had such a good hatch rate but if you want to keep them safe with very little loss its best to put them in a brooder.
A Poult its first 1 to 2 weeks old is a very fragile thing the mother will take the Poults out to feed and if in the first 1 to 2 weeks the Poults gets damp or chilled it can kill them.
Still not knowing were you live or not knowing what kind of predators Therese more loss there.
When relocating new bought adult birds of any kind some people would say keep them in the Pen for two weeks to get use to there new living area.
Me I would keep them up for 3 to 4 weeks and keep and eye on them for the first few days free ranging.
If there are wild Flocks of Turkeys in your area your Hen might have jumped the fence so to speak and is now living the wild life.
I have never seen wild Turkeys in the area I live and this year a wild Hen started Hanging around the Pen looking for a Boy friend.
I don't know how friendly your Turkeys are but I have trained my Red Bourbons with table scraps and bread and Biscuits they love bread of any kind.
I would let them free range and as soon as I would let them out I would yell Turkey Turkey and throw out the Treats after awhile I did not even have to call them they would hear the back screen door slam and come a running,
As you said them birds are not cheap thats why I am very protective of my flock and as much I like wild life I cant afford to feed the local wild life.
Best of luck to you and I hope I was of some help.
P.S. Turkeys are addictive