I assume you planted Oaks which are great for turkeys. Have you considered planting some nesting habitat?
Warm season grasses are great, bluestem, switch grass, indian grass, I liked planting it and then surrounding it with a perimeter of clover.
Burn the grass every other year or so prior to nesting season. Had a farm with acres of it scattered around and would rotate the fire so there was always standing grass somewhere.
Nuttall oaks grow quick and I know sawtooth produce mast quickly, not sure which produces acorns quicker but I think it is the sawtooth?