I would start a Muskie stocking program and start off heavy to the shad back under control.
Muskie will not reproduce and they will hunt down the gizzard shad.
For your situation, stock 3 per acre ASAP. Then stock one or two per acre every year until the shad are under control and you are infested with 15+ lb muskie!
Also for your consideration: Tiger Muskie grow faster and dont live as long as pure strain muskie. If the shad population gets back under control and you dont want the muskie anymore, dont stock them anymore and ecourage folks to harvest them! Muskie will hunt down all the gizzard shad before they will hunt for other gamefish. Also once the big shad are gone, Hybrid Striped Bass do a better job at hunting down the yoy gizzards than LMB do.
