I had a tract thinned every 3rd row about 4 years ago. The first year, had lots of turkeys. The second year I burned it and had tons of turkeys. The third year it grew up in briars, volunteer pines, and fennel and had very few turkeys. This year it is so grown up with briars, volunteer pines, and fennel that I really can't hunt.
The forestry service was trying to burn in March or April but decided there isn't enough fuel on the ground to kill all the volunteer pines. So it'll be a grown u0 mess for another year until there is sufficient fuel for a good burn.
My point is, I think under-story management beyond the thinning is more important than how much it is thinned. If a turkey can't move through the under-story, it won't matter how thin or thick the canopy above is. Just my experience