I don't think you need to shoot through the mesh at turkeys. The way I understand it, you don't need the mesh for turkeys, only for deer. The turkeys don't get spooked by the "black hole" effect like deer do. I never use my mesh when I turkey hunt and I have never had a problem.

Hit em' high watch em' die. Hit em' low watch em' go! Most people shoot turkeys to low and don't end up getting their vitals.

I carry a Gobbler Guillotine and 3 Wasp Jak-Hammers. If they're close they get decapitated and if they are beyond 20 yards, they get a mechanical. I have one Jak-Hammer that has killed 3 birds with the same blades. I just clean em' up and shoot em' again.

Good luck!