The Gizzards are eating the base of the food pyramid for the rest of the fish in the lake. A low dose of Rotenone might be beneficial. That will kill a lot of the Gizzards but very few of the other fish.

The LMB in the survey are only able to eat the smaller Gizzard shad and not the adults. A Gizzard shad can grow from hatching to being larger than the LMB in the survey can eat in less than a year. Without something in there to help hammer the Gizzard shad, the lake will slowly decline because they are eating a lot of food that would be going to growing the small panfish.

If it was legal to stock Hybrid Striped Bass in there, that is what I'd do - on the order of 20 or so per surface acre. They will not reproduce in there, and after they are 5#-7+# then you can start allowing some to be removed. You could stock the HSB at 4"-6" fish. Bigger than a lot of the bass could eat but they'd still be able to target the small GSD in there.

There is a local lake that is 360 acres. The last net survey that the DNR did showed 60% of the fish in the lake by weight were Gizzard Shad.

If the bass are eating the fish pellets, look at buying some Stubby Steve's pellets to fish with. The bass will hit those. https://stubbysteves.mybigcommerce.com/brown-fish-food-pellet/