I've been hunting public land last couple years after my lease got sold out from under me with no notice, but I also hunt the out of the way areas of it that are accessible by water only, so usually have 500-1500acres to myself because of how much of a pain the access to them is. Its a matter of paddling at least 2 miles, the last half mile of which has to be done by kayak or canoe due to sunken trees and shallows that won't allow a powered boat through, then another 1/4 mile of trekking through mud that makes me wish I was wearing snow shoes to prevent sinking, and then the hunting area begins. It's good hunting, but also a royal pain in the neck to get to, which is what keeps this area very rarely used. Even the rangers say they refuse to go there. Now the other areas at this lake that they allow hunting on, I try to avoid for the same reason you do. We haven't had any serious injuries, but there have been enough close calls that I treat the few hunts I have gone on there more like military patrols, making sure I am not seen or heard unless I take a shot at game. And then recover my game and sneak back out. I use the area that is a pain to get to for safety and so I don't have to hunt like a poacher would while still following game laws.
I do wish you the best of luck, as getting that turkey would be the perfect reward for all the work you have done to get everything in place. I know I will be trying if I find a place to hunt this spring.